Solution: 2019 Fall Final - 16

Author: Michiel Smid

Question

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

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

(a)

3/10

(b)

1/3

(c)

1/2

(d)

2/3

Let's determine $B$
There are 3 numbers divisible by 3, which are $ { 3, 6, 9 } $: 3
$ |B| = 3 $
Let's determine $A \cap B$
There is only 1 number that is both even and divisible by 3, which is 6: 1
$ |A \cap B| = 1 $

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