Question

​Multiple-choice questions each have four possible answers

left parenthesis a comma b comma c comma d right parenthesis(a, b, c, d)​,

one of which is correct. Assume that you guess the answers to three such questions.

a. Use the multiplication rule to find P(WWCWWC​),where C denotes a correct answer and W denotes a wrong answer.

​P(WWCWWC​)equals ???

​(Type an exact​ answer.

Answer 1

Solution

‘Multiple-choice questions each have four possible answers’ and ‘you guess the answers’ =>

The probability of the guessed answer being correct is P(C) = ¼ and it being wrong is P(W) = ¾.

Since answering is by guess, answer for each question is independent of the answer(s) for other questions. Hence, multiplicative rule of probability can be applied.

Thus, P(WWCWWC​)

= P(W) x P(W) x P(C) x P(W) x P(W) x P(C)

= (¾)(¾)(¼)(¾)(¾)(¼)

= 81/4096 = 0.0198 Answer

DONE

[Going beyond,

The above answer is for that particular order of wrong and correct answers. But, if the question were more generalized asking for the probability of 3 correct answers and 3 wrong answers, the above answer would be multiplied by 20, where 20 is the number of permutations of 3W’s and 3C’s which is (6!)/{(3!)(3!)}]