Question

Multiple-choice questions each have 6 possible answers, one of which is correct. Assume that you guess the answers to 5 such questions. Use the multiplication rule to find the probability that the first four guesses are wrong and the fifth is correct. That is, find P(WWWWC), where C denotes a correct answer and W denotes a wrong answer. '(round answer to 4 decimal places) P(WWWWC) =

Answer 1

The probability that the first four guesses are wrong and the fifth is correct (P(WWWWC)) is approximately 0.0804 when rounded to four decimal places.

Step-by-step explanation:

To calculate the probability that the first four guesses are wrong and the fifth is correct (P(WWWWC)), we use the multiplication rule for independent events. Since there are 6 possible answers for each question and only one is correct, the probability of guessing incorrectly (W) on one question is 5/6, and the probability of guessing correctly (C) is 1/6.

The multiplication rule states that for independent events, the probability of all events occurring is the product of their individual probabilities. Therefore, P(WWWWC) can be calculated as:

P(WWWWC) = P(W) × P(W) × P(W) × P(W) × P(C)
= (5/6) × (5/6) × (5/6) × (5/6) × (1/6)
= (625/1296) × (1/6)
= 625/7776

When rounded to four decimal places, the probability is:

P(WWWWC) ≈ 0.0804