Question

Jackson collects 4-sided, 6-sided, and 8-sided dice in different colors. He keeps all his dice in a jar.
The probability that a die selected randomly from the jar has 4 sides is
1
3
.
The probability that a die selected randomly from the jar is blue is
5
12
.
The probability that a die selected randomly from among all the blue dice has 4 sides is
3
5
.
What is the probability that a die selected randomly from among all the 4-sided dice is blue?
Write your answer as a fraction or decimal. Do not round.

Answer 1

Let B = blue and F = 4-sided.

P(F ∩ B) = P(B)·P(F | B) = (5/12)·(3/5) = 1/4.

Then P(B | F) = P(F ∩ B)/P(F) = (1/4)/(1/3) = 3/4.