Solution: 2016 Fall Final - 12

Author: Michiel Smid

Question

You roll a fair red die and a fair blue die, independently of each other. Let $r$ be the result of the red die and let $b$ be the result of the blue die. Define the events

A = "$r + b = 6$",
B = "$b = 4$".

What is $\Pr(B|A)$?

(a)

1/4

(b)

1/5

(c)

1/3

(d)

1/6

Solution

Let's determine A
The possible outcomes are (1,5), (2,4), (3,3), (4,2), (5,1)
$ |A| = 5 $
$ Pr(A) = \frac{5}{36} $
Let's determine $ A \cap B $
The possible outcomes are (2,4)
$ |A \cap B| = 1 $
$ Pr(A \cap B) = \frac{1}{36} $

$ Pr(B|A) = \frac{Pr(A \cap B)}{Pr(A)} $

$ Pr(B|A) = \frac{ \frac{1}{36}}{ \frac{5}{36}} $

$ Pr(B|A) = \frac{1}{5} $