A jar contains 11 large red marbles, four small red marbles, eight large blue marbles, and five small blue marbles.

Question

A jar contains 11 large red marbles, four small red marbles, eight large red marbles, and five small blue marbles. Find the probability of small marble given that it is a blue marble

Answer 1

A = small marble

B = blue marble

Want to find P(A|B) = probability small marble given it is a blue marble

P(A|B) = P(A and B)/P(B)

There are 28 marbles in the jar.

There are 5 small blue marbles in the jar

There are 13 blue marbles in the jar

P(A and B) = probability a small blue marble = 5/28

P(B) = probability a blue marble = 13/28

P(A|B) = 5/28 / 13/28 = 5/13