Worksheet: Solving Conditional Probability Problems

Q1:

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

Q2:

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

Q3:

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

Q4:

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

Q5:

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?

A
B
C
D

Q6:

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

Q7:

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.

A
B
C
D
E

Q8:

The table shows the data on all the students who tried out for the baseball team. Find the probability that Raymond is right-handed given that he tried out and did not make the team.

	Made the Team	Did Not Make the Team
Left-Handed	16	19
Right-Handed	23	12

A
B
C
D
E

Q9:

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

A
B1
C
D

Q10:

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

Q11:

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

	Swimming	Climbing	Abseiling
14 and Under	15	24	8
Over 14	18	32	24

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

A51%
B19.8%
C75%
D24.7%
E48%

Q12:

Consider the following Venn diagram.

Calculate the value of .

A
B
C
D
E

Q13:

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

A
B
C
D
E

Q14:

Andrew and Shirley 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 Shirley given that they are in the Class B?

	Class A	Class B	Class C	Total
Andrew	161	169	177	507
Shirley	147	195	152	494

A
B
C
D

Q15:

For two events and , , , and .

Work out the probability of given .

A
B
C
D
E

Work out the probability of given .

A
B
C
D
E

Q16:

The given Venn diagram shows the probabilities of events and occurring or NOT occurring in different combinations.

Calculate the value of .

A
B
C
D
E

Hence, calculate .

A
B
C
D
E

Calculate .

A
B
C
D
E

Are and independent events?

Ano
Byes