quizexe2 - probability that(1 he guessed exactly two...

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STAT 427 Quiz/Class Exercise 2: With Solution 1. Which of the following two numbers is larger: 93 30 ! or 93 31 ! Solution : ( 93 30 ) ( 93 31 ) = 93! 63!30! 93! 62!31! = 62!31! 63!30! = 62!31 × 30! 63 × 62!30! = 31 63 < 1 That is 93 30 ! < 93 31 ! 2. There are five multiple choice questions in an exam. Each question has four choices (A, B, C, or D). A student, totally unprepared, guessed each question randomly. What is the
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Unformatted text preview: probability that (1) he guessed exactly two questions correctly? (2) he guessed at least one question correctly? Solution : Let X denote the number of questions he guessed correctly (1) P ( X = 2) = 5 2 ! ± 1 4 ² 2 ± 1-1 4 ² 3 = . 264 (2) P ( X ≥ 1) = 1-P ( X = 0) = 1-(1-1 / 4) 5 = . 763 1...
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