Someone hands you a box of 23 chocolate-covered candies, telling you that 11 are vanilla creams and the rest are peanut butter. You pick candies at random and discover the first 3 you eat are all vanilla. Consider a result to be surprising if there is less than a5% chance of observing it given your expectations. Complete parts a through c below.

a) If there really were 11 vanilla and 12 peanut butter candies in thebox, what is the probability that you would have picked 3 vanillas in arow?

________ (Round to three decimal places asneeded.)

b) Do you think there really might have been 11 vanilla and 12 peanutbutter? Explain.

A. Possibly. Picking 3 vanillas in a row is not a surprising enough result to reject the statement that 11 are vanilla and 12 are peanut butter.

B. It is extremely unlikely that the first 3 candies picked would be vanilla if there were actually 11 vanilla and 12 peanut butter.

C. Almost definitely. Picking 3 vanillas is a very probable outcome if there really were 11 vanilla and 12 peanut butter.

D. Without picking all of oneflavor, there is no indication whether or not there really might have been 11 vanilla and 12 peanut butter.

c) Would you continue to believe that there really were 11 vanilla and 12 peanut butter candies in the box if the next 2 you try are alsovanilla? Explain. Select the correct choice belowand, ifnecessary, fill in the answer box to complete your choice.

A. No, since the probability of picking 5 vanillas in a row if there really were 11 vanilla and 12 peanut butter candies in the box is ________(Round to three decimal places asneeded.)

B. Yes, since the probability of picking 5 vanillas in a row if there really were 11 vanilla and 12 peanut butter candies in the box is _______.

(Round to three decimal places asneeded.)

C. Without picking morecandies, there is no indication whether or not there really might have been 11 vanilla and 12 peanut butter.