Conditional Probability

Question 1

How do you calculate the probability of A given B?

Answer 1

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

Question 2

Example 1 -

The Venn diagram shows the number of teachers who own cats (C) and dogs (D)

Cat:12
Dog:16
Both:2
Neither:5
a. Calculate P(C|D)
b. Calculate P(D|C')

Answer 2

a. P(CnD)/P(D)=2/35 divided by 18/35.Cancels out to 2/18

b. P(DnC’)/P(C’)=16/35 divided by 21/35=16/21

Question 3

Example 2 -

In New York, 48% of all teenagers own a skateboard. 39% of all teenagers own a skateboard and roller blades. What is the probability a teenager owns roller blades given they own a skateboard?

Answer 3

P(RB|S)=P(RBnS)/P(S)=39%/48%
=39/100 divided by 48/100
=39/48

Question 4

Example 3 -

In a room there are 25 people
4 of the people reading are wearing glasses
10 of people who are NOT reading are wearing glasses
3 people are not reading or wearing glasses

Given they are not wearing glasses, what is the probability of a chosen person reading?

Answer 4

Reading:8
Glasses:10
Both:4
Neither:3

P(R|G’)=8/25 divided by 11/25=8/11