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Worksheet: Probability of Unions, Intersections, and Complements
Q2:
Suppose that and are two events. Given that ,, and , find .
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Q3:
Suppose and are two events with probabilities and . Given that , determine the probability that at least one of the events and occurs.
Q4:
Suppose that and are two events with probabilities and . Given that , determine .
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Q5:
Suppose and are two events with probabilities and . Given that , determine the probability that only one of the events and occurs.
Q6:
Suppose , , and are three mutually exclusive events in a sample space . Given that , , and , find .
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Q7:
Suppose and are two events with probability and . Given that , what is the probability that at least one of the events does not occur?
Q8:
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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Q9:
Suppose and are events. Given that , , , and , find the value of .
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Q10:
Suppose and are two events with probabilities and . Given that , determine .
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Q11:
Suppose and are events. Given that , ,, and , find the value of .
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Q12:
Suppose and are two events in a random experiment. Given that , , and , find .
Q13:
Suppose and are two events with probabilities and . Given that and , find the value of .
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Q14:
A ball is drawn at random from a bag containing 94 balls each with a unique number from 1 to 94. Suppose is the event of drawing an odd number and is the event of drawing a prime number. Find .
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Q15:
Suppose and are two events. Given that and , find .
Q16:
Suppose and are events in the sample space of an experiment. Given that and , find the value of .
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Q17:
Suppose and are two events. Given that , , and , find .
Q18:
Suppose and are two events with probabilities and . Given that , determine .
Q19:
and are two events in a sample space of a random experiment where , , and . Find .
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Q20:
Suppose and are two events. Given that , , and , determine .
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Q21:
Denote by and two events with probabilities and . Given that , find .
Q22:
Suppose and are events such that . Determine .
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Q23:
Given that and are two events in the sample space of a random experiment, where , determine .
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Q24:
Denote by and two events with probabilities and . Given that , find .
Q25:
Suppose and are two events. Given that , , and , find .
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