Answered: Problem 1. When P(A) = 1/3, P(B) = 1/2 an... |24HA

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8.1.0599ms45MBGET college-homework-library/{category}/{subject}/{id}

Booting (415ms)time
Application (184ms)time
1 x Booting (69.32%)
415ms
1 x Application (30.68%)
184ms

Illuminate\Routing\Events\Routing (1.47ms)
Illuminate\Routing\Events\RouteMatched (657μs)
Illuminate\Foundation\Events\LocaleUpdated (6.46ms)
eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (243μs)
eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (255μs)
Illuminate\Database\Events\ConnectionEstablished (1.31ms)
Illuminate\Database\Events\StatementPrepared (7.38ms)
Illuminate\Database\Events\QueryExecuted (1.19ms)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (101μs)
eloquent.booting: App\Models\Subject (59μs)
eloquent.booted: App\Models\Subject (49μs)
Illuminate\Database\Events\StatementPrepared (1.53ms)
Illuminate\Database\Events\QueryExecuted (942μs)
eloquent.retrieved: App\Models\Subject (182μs)
eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (146μs)
eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (59μs)
Illuminate\Database\Events\StatementPrepared (681μs)
Illuminate\Database\Events\QueryExecuted (3.18ms)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (90μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (20μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (11μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (11μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (8μs)
eloquent.booting: App\Models\SubjectCat (418μs)
eloquent.booted: App\Models\SubjectCat (55μs)
Illuminate\Database\Events\StatementPrepared (802μs)
Illuminate\Database\Events\QueryExecuted (1.02ms)
eloquent.retrieved: App\Models\SubjectCat (125μs)
Illuminate\Cache\Events\CacheHit (14.71ms)
Illuminate\Cache\Events\CacheMissed (186μs)
Illuminate\Database\Events\StatementPrepared (788μs)
Illuminate\Database\Events\QueryExecuted (8.29ms)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (84μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (21μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (12μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (11μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (9μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (11μs)
Illuminate\Database\Events\StatementPrepared (697μs)
Illuminate\Database\Events\QueryExecuted (888μs)
eloquent.retrieved: App\Models\Subject (100μs)
Illuminate\Cache\Events\KeyWritten (838μs)
Illuminate\Database\Events\StatementPrepared (1.33ms)
Illuminate\Database\Events\QueryExecuted (1000μs)
Illuminate\Database\Events\StatementPrepared (740μs)
Illuminate\Database\Events\QueryExecuted (942μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (41μs)
Illuminate\Database\Events\StatementPrepared (804μs)
Illuminate\Database\Events\QueryExecuted (988μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (46μs)
Illuminate\Cache\Events\CacheHit (380μs)
creating: homework.show (240μs)
composing: homework.show (126μs)
creating: components.breadcrumbs (238μs)
composing: components.breadcrumbs (110μs)
Illuminate\Database\Events\StatementPrepared (1.06ms)
Illuminate\Database\Events\QueryExecuted (845μs)
eloquent.retrieved: App\Models\SubjectCat (76μs)
Illuminate\Cache\Events\CacheMissed (3.44ms)
Illuminate\Database\Events\StatementPrepared (705μs)
Illuminate\Database\Events\QueryExecuted (983μs)
eloquent.retrieved: App\Models\SubjectCat (93μs)
Illuminate\Cache\Events\KeyWritten (480μs)
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Illuminate\Cache\Events\CacheHit (191μs)
Illuminate\Cache\Events\CacheHit (279μs)
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Illuminate\Cache\Events\CacheHit (194μs)
Illuminate\Cache\Events\CacheHit (320μs)
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Illuminate\Cache\Events\CacheHit (206μs)
Illuminate\Cache\Events\CacheHit (175μs)
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Illuminate\Cache\Events\CacheHit (171μs)
Illuminate\Cache\Events\CacheMissed (2.26ms)
Illuminate\Database\Events\StatementPrepared (575μs)
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eloquent.retrieved: App\Models\SubjectCat (84μs)
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Illuminate\Cache\Events\CacheHit (282μs)
Illuminate\Cache\Events\CacheHit (232μs)
Illuminate\Cache\Events\CacheHit (196μs)
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Illuminate\Cache\Events\CacheHit (210μs)
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eloquent.retrieved: App\Models\SubjectCat (81μs)
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Illuminate\Cache\Events\CacheHit (178μs)
Illuminate\Cache\Events\CacheHit (592μs)
Illuminate\Cache\Events\CacheHit (199μs)
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Illuminate\Cache\Events\CacheHit (175μs)
Illuminate\Cache\Events\CacheHit (226μs)
Illuminate\Cache\Events\CacheHit (195μs)
Illuminate\Cache\Events\CacheHit (199μs)
Illuminate\Cache\Events\CacheHit (249μs)
Illuminate\Cache\Events\CacheHit (194μs)
Illuminate\Cache\Events\CacheHit (184μs)
Illuminate\Cache\Events\CacheHit (210μs)
Illuminate\Cache\Events\CacheHit (190μs)
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Illuminate\Cache\Events\CacheHit (182μs)
Illuminate\Cache\Events\CacheHit (265μs)
Illuminate\Cache\Events\CacheHit (210μs)
Illuminate\Cache\Events\CacheHit (198μs)
Illuminate\Cache\Events\CacheHit (186μs)
Illuminate\Cache\Events\CacheHit (287μs)
Illuminate\Cache\Events\CacheHit (185μs)
Illuminate\Cache\Events\CacheHit (196μs)
Illuminate\Cache\Events\CacheHit (183μs)
Illuminate\Cache\Events\CacheHit (197μs)
Illuminate\Cache\Events\CacheHit (182μs)
Illuminate\Cache\Events\CacheHit (195μs)
Illuminate\Cache\Events\CacheHit (183μs)
Illuminate\Cache\Events\CacheHit (197μs)
Illuminate\Cache\Events\CacheHit (222μs)
Illuminate\Cache\Events\CacheHit (200μs)
Illuminate\Cache\Events\CacheHit (180μs)
Illuminate\Cache\Events\CacheHit (198μs)
Illuminate\Cache\Events\CacheHit (165μs)
Illuminate\Cache\Events\CacheHit (183μs)
Illuminate\Cache\Events\CacheHit (159μs)
Illuminate\Cache\Events\CacheHit (248μs)
Illuminate\Cache\Events\CacheHit (224μs)
Illuminate\Cache\Events\CacheMissed (190μs)
Illuminate\Database\Events\StatementPrepared (594μs)
Illuminate\Database\Events\QueryExecuted (849μs)
eloquent.retrieved: App\Models\SubjectCat (81μs)
Illuminate\Cache\Events\KeyWritten (770μs)
Illuminate\Cache\Events\CacheHit (347μs)
Illuminate\Cache\Events\CacheHit (199μs)
Illuminate\Cache\Events\CacheHit (168μs)
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Illuminate\Cache\Events\CacheHit (181μs)
Illuminate\Cache\Events\CacheMissed (142μs)
Illuminate\Database\Events\StatementPrepared (593μs)
Illuminate\Database\Events\QueryExecuted (808μs)
eloquent.retrieved: App\Models\SubjectCat (71μs)
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Illuminate\Cache\Events\CacheHit (207μs)
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Illuminate\Cache\Events\CacheHit (187μs)
Illuminate\Cache\Events\CacheMissed (206μs)
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Illuminate\Database\Events\QueryExecuted (842μs)
eloquent.retrieved: App\Models\SubjectCat (115μs)
Illuminate\Cache\Events\KeyWritten (301μs)
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Illuminate\Cache\Events\CacheHit (167μs)
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311 x Illuminate\Cache\Events\CacheHit (14.24%)	85.33ms
20 x Illuminate\Database\Events\QueryExecuted (4.79%)	28.71ms
20 x Illuminate\Database\Events\StatementPrepared (4.05%)	24.25ms
11 x Illuminate\Cache\Events\KeyWritten (1.34%)	8.03ms
11 x Illuminate\Cache\Events\CacheMissed (1.3%)	7.77ms
1 x Illuminate\Foundation\Events\LocaleUpdated (1.08%)	6.46ms
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960μstwenty4_siteSubject.php#100

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Problem 1. When P(A) = 1/3, P(B) = 1/2 and P(A U B) = 3/4 what is...

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