# Lesson Worksheet: Operations on Events Mathematics

In this worksheet, we will practice finding the probabilities of the complement, intersection, and union of events.

Q1:

Denote by and two events with probabilities and . Given that , find .

Q2:

Denote by and two events with probabilities and . Given that , find .

Q3:

Suppose and are two events with probability and . Given that , what is the probability that at least one of the events does not occur?

Q4:

Suppose and are two events with probabilities and . Given that , determine .

Q5:

Suppose that and are two events with probabilities and . Given that , determine .

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Q6:

Suppose and are events such that . Determine .

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Q7:

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

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Q8:

A group of 68 school children completed a survey asking about their television preferences. The results show that 43 of the children watch channel , 26 watch channel , and 12 watch both channels. If a child is selected at random from the group, what is the probability that they watch at least one of the two channels?

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Q9:

Suppose and are events. Given that , , , and , find the value of .

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Q10:

Suppose and are events. Given that , ,, and , find the value of .

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Q11:

Suppose and are two events with probabilities and . Given that and , find the value of .

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Q12:

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

Q13:

A bag contains 15 blue balls and 20 red balls. A ball is chosen at random and the color is recorded. The ball is then replaced and another ball is chosen at random from the bag. What is the probability of both chosen balls being blue?

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Q14:

Suppose that and are two mutually exclusive events. Given that and , determine .

Q15:

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

Q16:

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

Q17:

Suppose that and are events with probabilities and . Given that and , find the value of .

Q18:

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

Q19:

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

Q20:

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

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Q21:

The diagram represents the sample space and the events , , and . Determine . • A
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Q22:

Out of a group of 100 people, 46 have dogs, 41 have cats, and 28 have rabbits. 12 of the people have both dogs and cats, 10 have both cats and rabbits, and 9 have both dogs and rabbits. 8 of the people have dogs, cats, and rabbits.

Find the probability of randomly selecting a person who has dogs, cats, and rabbits. Give your answer as a fraction in its simplest form.

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Find the probability of randomly selecting a person who only has dogs and rabbits. Give your answer as a fraction in its simplest form.

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Find the probability of selecting a person who has pets. Give your answer as a fraction in its simplest form.

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Find the probability of selecting a person who does not have pets. Give your answer as a fraction in its simplest form.

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Q23:

If and are events and is a subset of then which of the following is equal to ?

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Q24:

Given that and are two events in the sample space of a random experiment, where , determine .

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Q25:

I write a two-digit number by randomly picking each digit from the set , where digits can be repeated. Write the set that represents the event that the number is divisible by 3 and 6.

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