What is the probability that the second ball drawn is yellow?

Question

Assume that the box contains 12 balls: 3 red, 4 blue, and 5 yellow. As in the text, you draw one ball, note its color, and if it is yellow replace it. If it is not yellow you do not replace it. You then draw a second ball and note its color.
(1) What is the probability that the second ball drawn is yellow?

(2) What is the probability that the second ball drawn is red?

Answer 1

Katie,

(1) this is a conditional probability. Probability that event 2 will happen given that event 1 has happened. 

case 1: Probability that the first ball is yellow = 5/12

Probability that the second ball is yellow given that the first ball is yellow is  5/12
=> Probability that the second ball is yellow = (Probability that the first ball is yellow)(Probability that the second ball is yellow given that the first ball is yellow) = (5/12)(5/12)
Case 2: Probability that the first ball is not yellow = 7/12

Probability that the second ball is yellow given that the first ball is not yellow is 5/11

=> Probability that the second ball is yellow = (Probability that the first ball is not yellow)(Probability that the second ball is yellow given that the first ball is not yellow) = (7/12)(5/11)

Total probability = p1 + p2 = (5/12)(5/12) + (7/12)(5/11)

(2) pretty much the same applies for this but it way more involved: give 1st ball is/not yellow, given 1st ball is/not red.... I hope this helps.