The prince has searched all over his kingdom for the maiden who left the glass slipper at the ball. He will not recognize her by sight, but will use the abandoned slipper to determine who the maiden is. He arrives at the house where Cinderella and her four step-sisters live. The prince tries the slipper on one of the five sisters at random. If it does not fit, he will pick another sister to try it on, and so on, until he finds Cinderella.

a. What is the probability he finds Cinderella on the first try?

b. What is the probability he finds Cinderella on the third try?

c. What is the expected number of times he must try the slipper (in this house)?

Assuming he knows which foot it goes on, the probability he finds her on the first try is 1/5. Because there is her and her 4 stepsisters.

The probability he finds her on the third try:

He chooses one of the 4 stepsisters on the first attempt, 4/5.

On the second attempt, and since he already chose one he will not try her again, 3/4.

There are 3 left including Cinderella, 1/3

(4/5)(3/4)(1/3)=1/5 as well.

The probability is 1/5 regardless if he finds her first, second, third, fourth, or fifth.

The expectation is given by , that is the sum of the products of (1 x 1/5) + (2 x 1/5) +... + (5 x 1/5)