# Worksheet: Probability of Unions, Intersections, and Complements

In this worksheet, we will practice using unions, intersections, and complements of events in probability calculations.

**Q2: **

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

**Q3: **

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

**Q4: **

Suppose and are two events with probabilities and . Given that , determine the probability that at least one of the events and occurs.

**Q5: **

Denote by and two events in a sample space. Given that , , and , are the events and independent?

- Ayes
- Bno

**Q6: **

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

**Q7: **

Suppose , , and are three mutually exclusive events in a sample space . Given that , , and , find .

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**Q8: **

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

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**Q9: **

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

**Q10: **

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

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**Q11: **

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

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**Q12: **

Suppose and are two events with probabilities and . Given that , determine the probability that only one of the events and occurs.

**Q13: **

A ball is drawn at random from a bag containing 12 balls each with a unique number from 1 to 12. Suppose is the event of drawing an odd number and is the event of drawing a prime number. Find .

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**Q14: **

Suppose and are events in the sample space of an experiment. Given that and , find the value of .

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**Q15: **

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

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**Q16: **

and are two events in a sample space of a random experiment where , , and . Find .

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**Q17: **

Suppose and are events such that . Determine .

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**Q18: **

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

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**Q19: **

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

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**Q20: **

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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**Q21: **

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

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**Q22: **

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

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**Q23: **

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

**Q24: **

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

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**Q25: **

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