# Lesson Worksheet: Conditional Probability Mathematics

In this worksheet, we will practice calculating conditional probability using formulas and Venn diagrams.

Q1:

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

• A
• B
• C
• D

Q2:

On a street, there are 25 houses, of which 12 have a cat and 4 have both a cat and a dog. If a house has a cat, what is the probability that there is also a dog living there? Give your answer to three decimal places.

Q3:

A bag contains 16 balls numbered from 1 to 16. To select teams for a competition, 16 students took one ball each from the bag and those whose ball had an odd number were in Team A. Calculate the probability that a student choose the number 11 given that they are in Team A.

• A
• B
• C
• D

Q4:

In the final exam, of students failed chemistry, failed physics and failed both. What is the probability that a student passed physics given that they passed chemistry?

Q5:

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

Q6:

The probability that a student will pass an exam is 0.62. The probability that they travel abroad if they pass the exam is 0.5. What is the probability that they pass the exam and travel abroad?

Q7:

Two dice are rolled to give a pair of numbers. Given that both numbers are greater than 1, what is the probability that they are both equal to 2?

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• B
• C
• D

Q8:

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

Q9:

For two events and , , , and . Work out .

• A
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• E

Q10:

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

Q11:

On the street, 10 houses have a cat (C), 8 houses have a dog (D), 3 houses have both, and 7 houses have neither.

Find the total number of houses on the street. Hence, find the probability that a house chosen at random has both a cat and a dog. Give your answer to three decimal places.

• A0.167
• B0.818
• C0.2
• D0.12
• E0.136

Find the probability that a house on the street has either a cat or a dog or both. Give your answer to three decimal places.

• A0.6
• B0.682
• C0.136
• D0.318
• E0.818

If a house on the street has a cat, find the probability that there is also a dog living there.

• A0.136
• B0.375
• C0.364
• D0.682
• E0.3

Q12:

It has been found for two events and that , , and .

Work out .

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• B
• C
• D
• E

Work out .

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• B
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• D
• E

Work out .

• A
• B
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• D
• E

Q13:

For two events and , , , and . Find .

Q14:

The probability that event occurs is . If event does NOT occur, then the probability of event occurring is . What is the probability that event does NOT occur and event occurs?

• A
• B
• C
• D
• E

Q15:

For two independent events and , where and , calculate .

Q16:

Suppose and . The probability that event occurs and event also occurs is . Calculate , and then evaluate whether events and are independent.

• A, so they are independent.
• B, so they are not independent.
• C, so they are not independent.
• D, so they are independent.
• E, so they are not independent.

Q17:

Suppose and . The probability that event occurs and event also occurs is . Calculate , and then evaluate whether events and are independent.

• A;, so they are not independent.
• B;, so they are independent.
• C;, so they are not independent.
• D;, so they are not independent.
• E;, so they are independent.

Q18:

Mason and Liam are using their computers to take part in an online experiment on a website. When Mason presses the space bar on his keyboard, there is a probability that his screen turns blue. When Liam presses the space bar on his keyboard, there is a probability that his screen turns blue. If they both press their space bars, there is a chance that both of their screens turn blue. Are “Mason’s screen turning blue” and “Liam’s screen turning blue” independent events?

• ANo
• BYes

Q19:

Suppose and . The probability that neither event nor event occurs is . Calculate , and then evaluate whether events and are independent.

• A, so they are not independent.
• B, so they are independent.
• C, so they are not independent.
• D, so they are independent.
• E, so they are not independent.

Q20:

Consider the following Venn diagram. Calculate the value of .

• A
• B
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• D
• E

Q21:

The figure shows a Venn diagram with some of the probabilities given for two events and . Work out .

Work out .

Work out .

Q22:

The figure shows a Venn diagram with some of the probabilities given for two events and . Work out .

Work out .

Work out .

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• B
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• D
• E

Q23:

For two events and , , , and . Work out the value of in the Venn diagram.

Work out .

• A
• B
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• D
• E

Q24:

The given Venn diagram shows the probabilities of events and occurring or NOT occurring in different combinations. Calculate and , and then determine whether and are independent events.

• A and ;, so and are independent events.
• B and ;, so and are not independent events.
• C and ;, so and are not independent events.
• D and ;, so and are not independent events.
• E and ;, so and are independent events.

Q25:

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

• A
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• E

Hence, calculate .

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• E

Calculate .

• A
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• E

Are and independent events?

• AYes
• BNo