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Christina is randomly choosing three movies to take on vacation from nine action movies, seven science fiction movies, and four comedies. Which statement is true?
The probability that Christina will choose three comedies can be expressed as StartFraction 1 Over 4 C 3 EndFraction.
The probability that Christina will choose three action movies can be expressed as StartFraction 20 C 3 Over 9 C 3 EndFraction.
The probability that Christina will not choose all comedies can be expressed as 1 − StartFraction 4 C 3 Over 20 C 4 EndFraction.
The probability that Christina will not choose all action movies can be expressed as 1 − StartFraction 9 C 3 Over 20 C 3 EndFraction.
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GPT-5 mini
AI
Only the fourth statement is true.
Reason: There are 20 movies total, so the probability of choosing three action movies is (9 choose 3)/(20 choose 3). Thus the probability of not choosing all action movies is 1 − (9 choose 3)/(20 choose 3). The other three expressions use incorrect numerators/denominators or are inverted.
Reason: There are 20 movies total, so the probability of choosing three action movies is (9 choose 3)/(20 choose 3). Thus the probability of not choosing all action movies is 1 − (9 choose 3)/(20 choose 3). The other three expressions use incorrect numerators/denominators or are inverted.
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