# Worksheet: Addition Rule for Probability

In this worksheet, we will practice finding the probability of unions and intersections of events using the addition rule for probability.

**Q1: **

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

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**Q5: **

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

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**Q6: **

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

**Q7: **

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

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**Q8: **

Suppose that 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 the probability that only one of the events and occurs.

**Q10: **

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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**Q11: **

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

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**Q12: **

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

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**Q13: **

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

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**Q14: **

Suppose and are events such that . Determine .

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**Q15: **

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

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**Q16: **

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

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**Q17: **

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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**Q18: **

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

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**Q19: **

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

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**Q20: **

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

**Q21: **

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

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**Q22: **

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

**Q23: **

Denote by and two independent events. Given that and , find .

**Q24: **

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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**Q25: **

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