Solution: 2014 Fall Final - 16

Author: Michiel Smid

Question

We choose an element $x$ uniformly at random from the set $\{1,2,3,\dots,10\}$. Define the events

What is the conditional probability $\Pr(A|B)$?

(a)

3/10

(b)

2/3

(c)

1/2

(d)

1/3

Let A = Event that $x$ is even
A occurs when we choose an even number from the set ${2, 4, 6, 8, 10}$
$ |A| = 5 $
Let B = Event that $x$ is divisible by 3
B occurs when we choose a number from the set ${3, 6, 9}$
$ |B| = 3 $
Let $A \cap B$ = Event that $x$ is even and divisible by 3
$ |A \cap B| = 1 $

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

$ Pr(A|B) = \frac{1}{3} $