# Lesson Worksheet: Operations on Events Mathematics • 10th Grade

In this worksheet, we will practice finding the probabilities of the complement, 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:

Suppose and are events such that . Determine .

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Q3:

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

Q4:

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

Q5:

Suppose and are two events with probability and . Given that , what is the probability that neither of the events occur?

Q6:

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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Q7:

and are two events in a sample space of a random experiment and . The probability that at most one of or occurs is 0.56. The probability that at least one of or occurs is 0.68. Find the probability that occurs OR does not occur.

Q8:

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

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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 in a sample space which consists of equally likely outcomes. Given that the number of outcomes in is 3, the number of outcomes in is 11, the number of outcomes common to both and is 2, and , find .

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