Multiple Choice Test: Binomial Probability

Date: 08/05/97 at 18:55:12
From: Heather
Subject: Multiple choice test

A multiple choice test consists of 9 questions with 5 choices for each
answer. If a student guesses randomly, find the probability of each of 
the following events:

  1. The student gets 5 correct
  2. The student gets at least 5 correct
  3. The student gets 2 correct answers
  4. The student gets fewer than 3 correct answers.

Date: 08/06/97 at 11:55:26
From: Doctor Anthony
Subject: Re: Multiple choice test

This is binomial probability with  n = 9,  p = 1/5,  q = 4/5

  1. P(5) = 9C5 (1/5)^5 (4/5)^4 = 0.016515

  2. At least 5 is = P(5) + P(6) + P(7) + P(8) + P(9)

     P(6) = 9C6 (1/5)^6 (4/5)^3 = .0027525   and so on.....

  3. P(2) = 9C2 (1/5)^2 (4/5)^7 = 0.301989

  4. P(< 2) = P(0) + P(1) 

       P(0) =  (4/5)^9 = 0.1342177

       P(1) = 9C1 (1/5) (4/5)^8  = 0.301989

So   P(<2) = Sum of these = 0.43621 

-Doctor Anthony,  The Math Forum
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