Question
1. For the distribution of student suspensions from school, assume that these can be used to derive empirical estimates of probabilities.
a. What is the probability that a randomly selected student will be suspended sometime during the year?
b. What is the probability that a randomly selected student will be suspended at least twice during the year?
c. What is the probability that a randomly selected student will be suspended at least twice during the given that he or she is suspended at least once?
d. If two students (Student A and Student B) are selected at random, what is the probability that Students A and B are both are suspended sometime during the year? Are these events independent? Explain.
e. If two students (Student A and Student B) are selected at random, what is the probability that either Student A or Student B is suspended sometime during the year? Are these events mutually exclusive? Explain.

2. A taxi involved in a night-time hit-and-run accident was identified by an eyewitness as being blue. Suppose that in the city, 85% of the cabs are blue and 15% are green. Tests indicated that the witness (in conditions of poor lighting) was able to distinguish correctly the colors blue and green 80% of time. What is the probability that the cab was indeed blue given the eyewitness testimony?

3. In a particular state, 90% of murderers are male, and 70% of these murderers kill males. Female killers also tend to kill men—4 out of 5 kill men. The likelihood of receiving a life sentence varies by gender combination according to the table below (e.g., the probability that a male offender who killed a male victim is sentenced to life is .70.):

Offender Sex

Victim Sex

Probability of a life sentence

Male

Male

0.70

Male

Female

0.90

Female

Male

0.10

Female

Female

0.20

a. What is the probability that a randomly selected lifer is male?
b. What is the probability that a randomly selected lifer killed a female?
c. What is the probability that a randomly selected lifer Is male or killed a female?
d. What is the probability that a randomly selected lifer Is male and killed a female?
e. What is the probability of male killers being sentenced to life?
f. What is the probability of female killers being sentenced to life?
g. What is the probability that a randomly selected killer is sentenced to life?

4. Suppose that 90% of adults get married at least once, that 40% of first marriages end in divorce, that 70% of those marry for the second time, that 50% of second marriages end in divorce, that 35% of the double divorcees marry for the third time, that 75% of third marriages end in divorce, that 10% of those marry a fourth time, and for them the fourth time is a charm as 80% say with their fourth spouse. For a population of 1,000 people, how many marriages and how many divorces would you expect?
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      • Illuminate\Cache\Events\CacheHit (113μs)
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      • Illuminate\Cache\Events\CacheHit (219μs)
      • Illuminate\Cache\Events\CacheHit (130μs)
      • Illuminate\Cache\Events\CacheHit (100μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (123μs)
      • Illuminate\Cache\Events\CacheHit (127μs)
      • Illuminate\Cache\Events\CacheHit (98μs)
      • Illuminate\Cache\Events\CacheHit (125μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (120μs)
      • Illuminate\Cache\Events\CacheHit (193μs)
      • Illuminate\Cache\Events\CacheHit (219μs)
      • Illuminate\Cache\Events\CacheHit (108μs)
      • Illuminate\Cache\Events\CacheHit (123μs)
      • Illuminate\Cache\Events\CacheHit (102μs)
      • Illuminate\Cache\Events\CacheHit (207μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheMissed (189μs)
      • Illuminate\Database\Events\StatementPrepared (808μs)
      • Illuminate\Database\Events\QueryExecuted (856μs)
      • eloquent.retrieved: App\Models\SubjectCat (130μs)
      • Illuminate\Cache\Events\KeyWritten (262μs)
      • Illuminate\Cache\Events\CacheHit (150μs)
      • Illuminate\Cache\Events\CacheHit (226μs)
      • Illuminate\Cache\Events\CacheHit (119μs)
      • Illuminate\Cache\Events\CacheHit (126μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (116μs)
      • Illuminate\Cache\Events\CacheHit (133μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (146μs)
      • Illuminate\Cache\Events\CacheHit (101μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (140μs)
      • Illuminate\Cache\Events\CacheHit (121μs)
      • Illuminate\Cache\Events\CacheHit (99μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • creating: site.layouts.app (347μs)
      • composing: site.layouts.app (16μs)
      • creating: components.canonical (655μs)
      • composing: components.canonical (84μs)
      • creating: components.open-graph (160μs)
      • composing: components.open-graph (49μs)
      • creating: site.headers.header (294μs)
      • composing: site.headers.header (58μs)
      • Illuminate\Cache\Events\CacheHit (1.34ms)
      • creating: components.footer (61μs)
      • composing: components.footer (62μs)
      • Illuminate\Cache\Events\CacheHit (961μs)
      • Illuminate\Cache\Events\CacheMissed (429μs)
      • Illuminate\Database\Events\StatementPrepared (673μs)
      • Illuminate\Database\Events\QueryExecuted (959μs)
      • eloquent.retrieved: App\Models\SubjectCat (97μs)
      • Illuminate\Cache\Events\KeyWritten (326μs)
      • Illuminate\Cache\Events\CacheHit (223μs)
      • Illuminate\Cache\Events\CacheHit (201μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (118μs)
      • Illuminate\Cache\Events\CacheHit (117μs)
      • Illuminate\Cache\Events\CacheHit (318μs)
      • Illuminate\Cache\Events\CacheHit (236μs)
      • Illuminate\Cache\Events\CacheHit (210μs)
      • Illuminate\Cache\Events\CacheHit (136μs)
      • Illuminate\Cache\Events\CacheHit (202μs)
      • Illuminate\Cache\Events\CacheHit (226μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • creating: components.forms.contact-us (180μs)
      • composing: components.forms.contact-us (167μs)
      • creating: components.forms.get-started (129μs)
      • composing: components.forms.get-started (47μs)
      • creating: components.forms.free-tool-download (125μs)
      • composing: components.forms.free-tool-download (47μs)
      • creating: components.forms.claim-free-worksheet (148μs)
      • composing: components.forms.claim-free-worksheet (56μs)
      • creating: components.forms.tutor-subscription-waitlist (99μs)
      • composing: components.forms.tutor-subscription-waitlist (41μs)
      • creating: components.forms.tutor-subscription-join (79μs)
      • composing: components.forms.tutor-subscription-join (49μs)
      • creating: components.forms.tutor-support (73μs)
      • composing: components.forms.tutor-support (38μs)
      • 311 x Illuminate\Cache\Events\CacheHit (17.49%)
        56.35ms
        20 x Illuminate\Database\Events\QueryExecuted (7.85%)
        25.30ms
        20 x Illuminate\Database\Events\StatementPrepared (7.38%)
        23.77ms
        11 x Illuminate\Cache\Events\CacheMissed (2.54%)
        8.18ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (2.32%)
        7.47ms
        11 x Illuminate\Cache\Events\KeyWritten (1.09%)
        3.50ms
        1 x Illuminate\Routing\Events\Routing (0.27%)
        877μs
        12 x eloquent.retrieved: App\Models\SubjectCat (0.24%)
        787μs
        1 x Illuminate\Database\Events\ConnectionEstablished (0.24%)
        760μs
        1 x creating: components.canonical (0.2%)
        655μs
        1 x eloquent.booting: App\Models\SubjectCat (0.12%)
        379μs
        1 x Illuminate\Routing\Events\RouteMatched (0.11%)
        366μs
        1 x creating: site.layouts.app (0.11%)
        347μs
        1 x creating: site.headers.header (0.09%)
        294μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.09%)
        280μs
        1 x creating: components.breadcrumbs (0.08%)
        265μs
        1 x creating: homework.show (0.07%)
        237μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.06%)
        185μs
        1 x creating: components.forms.contact-us (0.06%)
        180μs
        8 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.05%)
        171μs
        1 x composing: components.forms.contact-us (0.05%)
        167μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.05%)
        162μs
        1 x creating: components.open-graph (0.05%)
        160μs
        2 x eloquent.retrieved: App\Models\Subject (0.05%)
        151μs
        1 x creating: components.forms.claim-free-worksheet (0.05%)
        148μs
        1 x creating: components.forms.get-started (0.04%)
        129μs
        1 x creating: components.forms.free-tool-download (0.04%)
        125μs
        1 x composing: components.breadcrumbs (0.04%)
        118μs
        1 x composing: homework.show (0.03%)
        112μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.03%)
        99μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.03%)
        99μs
        1 x eloquent.booting: App\Models\Subject (0.03%)
        93μs
        1 x composing: components.canonical (0.03%)
        84μs
        1 x creating: components.forms.tutor-subscription-join (0.02%)
        79μs
        1 x creating: components.forms.tutor-support (0.02%)
        73μs
        1 x composing: components.footer (0.02%)
        62μs
        1 x creating: components.footer (0.02%)
        61μs
        1 x composing: site.headers.header (0.02%)
        58μs
        1 x composing: components.forms.claim-free-worksheet (0.02%)
        56μs
        1 x composing: components.open-graph (0.02%)
        49μs
        1 x composing: components.forms.tutor-subscription-join (0.02%)
        49μs
        1 x composing: components.forms.get-started (0.01%)
        47μs
        1 x composing: components.forms.free-tool-download (0.01%)
        47μs
        1 x eloquent.booted: App\Models\Subject (0.01%)
        42μs
        1 x eloquent.booted: App\Models\SubjectCat (0.01%)
        41μs
        1 x composing: components.forms.tutor-subscription-waitlist (0.01%)
        41μs
        1 x composing: components.forms.tutor-support (0.01%)
        38μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)
        38μs
        1 x composing: site.layouts.app (0%)
        16μs
      14 templates were rendered
      • 1x homework.showshow.blade.phpblade
      • 1x components.breadcrumbsbreadcrumbs.blade.phpblade
      • 1x site.layouts.appapp.blade.phpblade
      • 1x components.canonicalcanonical.blade.phpblade
      • 1x components.open-graphopen-graph.blade.phpblade
      • 1x site.headers.headerheader.blade.phpblade
      • 1x components.footerfooter.blade.phpblade
      • 1x components.forms.contact-uscontact-us.blade.phpblade
      • 1x components.forms.get-startedget-started.blade.phpblade
      • 1x components.forms.free-tool-downloadfree-tool-download.blade.phpblade
      • 1x components.forms.claim-free-worksheetclaim-free-worksheet.blade.phpblade
      • 1x components.forms.tutor-subscription-waitlisttutor-subscription-waitlist.blade.phpblade
      • 1x components.forms.tutor-subscription-jointutor-subscription-join.blade.phpblade
      • 1x components.forms.tutor-supporttutor-support.blade.phpblade
      uri
      GET college-homework-library/{category}/{subject}/{id}
      middleware
      web, utm.parameters
      controller
      App\Http\Controllers\HomeworkLibraryController@show
      namespace
      where
      as
      homework.show
      file
      app/Http/Controllers/HomeworkLibraryController.php:79-176
      20 statements were executed, 5 of which were duplicates, 15 unique. Show only duplicated36.67ms
      • Connection Establishedtwenty4_siteHomeworkLibraryController.php#91
        Backtrace
        • 13. app/Http/Controllers/HomeworkLibraryController.php:91
        • 14. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 15. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 16. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary` where `status` = 'published' and `price` > 0 and `solutionslibrary`.`id` = '41732' limit 1
        8.48mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
        • 0: published
        • 1: 0
        • 2: 41732
        Backtrace
        • 16. app/Http/Controllers/HomeworkLibraryController.php:97
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 19. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 20. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subjects` where `subjects`.`id` in (7)
        930μstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` in (41732)
        810μstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        970μstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 1
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 26. app/Http/Controllers/HomeworkLibraryController.php:105
        • 27. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 28. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 29. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • select * from `solutionslibrary` where `id` <> 41732 and `subject` = 7 and `status` = 'published' and `price` > 0 order by RAND() limit 6
        10.63mstwenty4_siteHomeworkLibraryRepository.php#30
        Bindings
        • 0: 41732
        • 1: 7
        • 2: published
        • 3: 0
        Backtrace
        • 14. app/Repositories/HomeworkLibraryRepository.php:30
        • 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 16. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 18. app/Repositories/HomeworkLibraryRepository.php:39
        • 19. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `subjects` where `subjects`.`id` in (7)
        900μstwenty4_siteHomeworkLibraryRepository.php#30
        Backtrace
        • 19. app/Repositories/HomeworkLibraryRepository.php:30
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 23. app/Repositories/HomeworkLibraryRepository.php:39
        • 24. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 41732 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        840μstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 41732
        • 1: question
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:58
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 41732 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc
        840μstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 41732
        • 1: teaser
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:69
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 41732 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc
        1.14mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 41732
        • 1: solution
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:80
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        870μstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 1
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 32. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 33. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 34. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
        • 35. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        940μstwenty4_siteSubject.php#100
        Bindings
        • 0: 1
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 3 limit 1
        980μstwenty4_siteSubject.php#100
        Bindings
        • 0: 3
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 4 limit 1
        920μstwenty4_siteSubject.php#100
        Bindings
        • 0: 4
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 10 limit 1
        1.29mstwenty4_siteSubject.php#100
        Bindings
        • 0: 10
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 33 limit 1
        1.01mstwenty4_siteSubject.php#100
        Bindings
        • 0: 33
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 11 limit 1
        920μstwenty4_siteSubject.php#100
        Bindings
        • 0: 11
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 5 limit 1
        960μstwenty4_siteSubject.php#100
        Bindings
        • 0: 5
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 34 limit 1
        1.13mstwenty4_siteSubject.php#100
        Bindings
        • 0: 34
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 31 limit 1
        1.08mstwenty4_siteSubject.php#100
        Bindings
        • 0: 31
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 36 limit 1
        1.03mstwenty4_siteSubject.php#100
        Bindings
        • 0: 36
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 28. view::components.footer:170
      App\Models\SubjectCat
      12SubjectCat.php
      App\Models\HomeworkLibrary\HomeworkLibraryFile
      8HomeworkLibraryFile.php
      App\Models\HomeworkLibrary\HomeworkLibrary
      7HomeworkLibrary.php
      App\Models\Subject
      2Subject.php
          _token
          4OuK8yW2aiBrqcoEByH4fWb1RA6VpLBN17XMgNaj
          utm_source
          direct
          redirectUrl
          /college-homework-library/Mathematics/General-Statistics/41732
          _previous
          array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Mathematics/Gen...
          _flash
          array:2 [ "old" => [] "new" => [] ]
          PHPDEBUGBAR_STACK_DATA
          []
          path_info
          /college-homework-library/Mathematics/General-Statistics/41732
          status_code
          200
          
          status_text
          OK
          format
          html
          content_type
          text/html; charset=UTF-8
          request_query
          []
          
          request_request
          []
          
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