# Lesson Worksheet: Operations on Events Mathematics

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

**Q1: **

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

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**Q2: **

The diagram represents the sample space and the events , , and . Determine .

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**Q3: **

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

**Q4: **

For two events and , , , and . Work out the probability of .

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**Q5: **

For two events and , , , and . Work out the probability of .

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**Q6: **

A survey was conducted on a group of 263 children to determine their favorite superheroes. The results are shown in the Venn Diagram. Find .

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**Q7: **

Mason spins two 4-sided spinners which are both numbered from 1 to 4. Let be the event that he spins two numbers with a product of 4 and let be the event that he spins two even numbers.

Find , giving your answer as a fraction in its simplest form.

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Find , giving your answer as a fraction in its simplest form.

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Find , giving your answer as a fraction in its simplest form.

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Determine the value of , giving your answer as a fraction in its simplest form.

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**Q8: **

The probability that a student passes their physics exam is 0.85. The probability that they pass their mathematics exam is 0.8. The probability that they pass both exams is 0.71. What is the probability that the student passes at least one of the two exams?

**Q9: **

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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**Q10: **

Students at a school must wear a sweatshirt or a blazer, and are allowed to wear both. In one class of 32 students, 12 students wear blazers, and 4 of the students who wear a blazer also wear a sweatshirt. Let be the event of randomly selecting a student from the class who wears a blazer and let be the event of randomly selecting a student from the class who wears a sweatshirt.

Find , giving your answer as a fraction in its simplest form.

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Find , giving your answer as a fraction in its simplest form.

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Find , giving your answer as a fraction in its simplest form.

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Determine the value of , giving your answer as a fraction in its simplest form.