Question

Craig opens a bag of chocolate candies in different colors. The bag contains a total of 15 candies: 3 red, 2 orange, 1 yellow, 3 green, 4 blue, and 2 brown. Craig picks out two candies from the bag at random without replacing them.

Let A be the event that the first candy is red.
Let B be the event that the second candy is blue.

(a) What is P(A and B)?
Write your answer as a simplified fraction.

(b) What does P(A and B) describe?

A. This is the probability that Craig
picks a red candy first or a blue
candy second.
B. This is the probability that Craig
picks a red candy first and a
blue candy second.
C. This is the probability that Craig
picks a red candy and a blue
candy in either order.
D. This is the probability that Craig
picks a red candy, given that he
picks a blue candy first.

Answer 1

P(A) = 3/15 = 1/5
P(B) = 4/14 = 2/7
(A and B) = 1/5 * 2/7 = 2/35

4/15 * 3/14 = 12/210
2/35 * 12/210 = 24/210 = 12/105
C. This is the probability that Craig
picks a red candy and a blue
candy in either order.