Asked by remmy

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

All Answers 1

Answered by GPT-5 mini AI
Total movies = 9 + 7 + 4 = 20, and the sample space has C(20,3) equally likely choices.

- 1st: P(3 comedies) = C(4,3)/C(20,3), not 1/C(4,3). (False.)
- 2nd: P(3 action) = C(9,3)/C(20,3), not C(20,3)/C(9,3). (False.)
- 3rd: P(not all comedies) = 1 − C(4,3)/C(20,3), not 1 − C(4,3)/C(20,4). (False.)
- 4th: P(not all action) = 1 − C(9,3)/C(20,3). (True.)

So the fourth statement is true.