Binomial model for guessed answers in a quiz: the expected number correct, an exact count and at most a given number
Binomial model for guessed answers in a quiz: the expected number correct, an exact count and at most a given number
6 marks
A quiz has \(12\) questions. Each question has four options, exactly one of which is correct. A student guesses the answer to every question, choosing each option with equal probability and independently of the other questions.
- Write down the expected number of correct answers.[1]
- Find the probability that the student gets exactly five answers correct.[2]
- Find the probability that the student gets at most two answers correct.[3]
Solution:
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Answer:(a) \(3\) (b) \(0.103\) (c) \(0.391\)
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