Question

The A.P. Statistics exam consists of a multiple-choice section in which each question has five choices. Sara estimates that she has a 75% chance of knowing each question. If she does not know the answer, she will randomly guess.

a) What is the probability of Sara getting a question correct?
b) The A.P. exam has 40 questions, how many might Sara expect to get correct?

Answer 1

a)
75% she knows for sure
Out of the remaining 25%, she has a 1/5 or 20% chance of getting it right. So,
1/4 x 1/5 x 100 = 5%
Total chance of getting a question right:
75 + 5 = 80%
b) If the total is 40, she can expect to get
80% x 40 = 32 questions correct.