Suppose that you have 12 tennis balls in a black box Each ti

Suppose that you have 12 tennis balls in a black box. Each time when you go to play tennis, you randomly pick 3 balls one by one (assume that you cannot see the ball until you pick it out of the box and once it is taken out of the box, it will not be put back into the box until the game is over). After the game, these three tennis balls are marked as

Solution

(a) What is the probability that the second ball you pick from the box is marked?

Two cases :
First ball = marked, second ball = marked
OR
First ball = unmarked, second ball = marked

P(marked , marked) = 3/12 * 2/11 = 1/22
P(unmarked, marked) = 9/12 * 3/11 = 9/44

So,P(2nd ball marked) = 1/22 + 9/44 =2/44 + 9/44 = 11/44 = 1/4

(b) What is the probability that all three balls you picked are never used?

P(all three unmarked) = (9/12)(8/11)(7/10) = 21/55

(c) What is the probability that only one ball out of three balls is marked?

P(1 marked, 2 unmarked) = (3C1)*(9C2) / 12C3 = (3 * 36) / 220 = 108/220 = 27/55

Answers are :

1/4
21/55
27/55