Applications of Probability — Test

Question 9 • Concepts in Probability and Statistics

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?

Answer

The probability that Christina will not choose all comedies can be expressed as 1 minus the fraction with numerator 4 cap c sub 3 and denominator 20 cap c sub 4 .

The probability that Christina will not choose all action movies can be expressed as 1 minus the fraction with numerator 9 cap c sub 3 and denominator 20 cap c sub 3 .

The probability that Christina will choose three action movies can be expressed as the fraction with numerator sub 20 mathrm cap c sub 3 and denominator sub 9 mathrm cap c sub 3 .

The probability that Christina will choose three comedies can be expressed as the fraction with numerator 1 and denominator sub 4 mathrm cap c sub 3 .

Explanation

There are 9 + 7 + 4 = 20 movies, so the total number of ways to choose 3 is C(20, 3). The number of ways to choose 3 action movies is C(9, 3), making the probability of choosing all action movies C(9, 3) / C(20, 3). Therefore, the probability of not choosing all action movies is 1 − C(9, 3) / C(20, 3), as stated in choice B.

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