Question

A QUESTION ON A PROFICIENCY TEST IS MULTIPLE CHOICE WITH 4 POSSIBLE ANSWERS, 1 OF WHICH IS CORRECT. ASSUMING THAT ALL RESPONSES ARE RANDOM GUESSES FIND THE PROBABILITY THAT AMOUNG 12 TEST SUBJECTS, EXACTLY 5 ANSWERS ARE CORRECT

Answer 1

In this scenario, there are only 2 possible outcomes. It is either the answer is correct or wrong.Since the outcomes are independent, it means that it is binomial probability. We would apply the binomial distribution formula which is expressed as

P(x) = nCx * p^x * q^(n - x)

where

n is the sample size

x is the number of successes

p is the probability of success

q = 1 - p = probability of failure

From the information given,

p = 1/4 = 0.25

q = 1 - 1/4 = 3/4 = 0.75

n = 12

x = 5

We want to find P(x = 5)

P(x = 5) = 12C5 * 0.25^5 * 0.75^(12 - 5)

P(x = 5) = 0.103

The probability that among 12 test subjects, exactly 5 answers are correct is 0.103

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