Use a binomial model for random multiple-choice answers.

Use a binomial model for random multiple-choice answers.

6 marks
ProbabilityQuestionBank.pdf

A multiple choice test consists of ten questions. Each question has five answers. Only one of the answers is correct. For each question, Jose randomly chooses one of the five answers.

  1. Find the expected number of questions Jose answers correctly.[1]
  2. Find the probability that Jose answers exactly three questions correctly.[2]
  3. Find the probability that Jose answers more than three questions correctly.[3]

Solution:

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Answer:\(P(X=3)=\binom{10}{3}(0.2)^3(0.8)^7=0.2013\), and \(P(X>3)=0.1209\).

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