Worksheet: Solving Conditional Probability Problems

Suppose that and are two events. Given that and , find .

Suppose that and are two events. Given that and , find .

Suppose that and are two events. Given that and , find .

Suppose that and are events with probabilities and . Given that , find .

240 people are taking science classes. There are 104 people studying chemistry, 132 people studying biology, and 68 of those are studying both. What is the probability that a person is studying Chemistry given that they are studying Biology?

Suppose that and are events in a random experiment. Given that and , find .

In a group of 96 people, 34 out of the 71 women have a smartphone, and 18 men do not have a smartphone. Determine the probability that a randomly picked smartphone owner in this group will be female.

Liam rolled a fair six-sided die. Determine the probability of him rolling a 6 or less given that he rolled an odd number.

For two events and , and . Determine the probability of .

The two-way table shows the ages and activity choices of a group of participants at a summer camp.

A child is selected at random. Given that they chose abseiling, find the probability that the child is over 14.

Consider the following Venn diagram.

Calculate the value of .

Suppose and . What is the probability that events and both occur?

Daniel and Jennifer are running for the presidency of the Students’ Union at their school. The votes they received from each of 3 classes are shown in the table. What is the probability that a student voted for Jennifer given that they are in the Class B?