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 .