Problem-Solving and Data AnalysisEasyProbability from a two-way frequency table
Problem-Solving and Data Analysis practice question
The table below shows the elective course chosen by each of the 80 students in a school's ninth and tenth grades.
Art Music Total
9th grade 14 26 40
10th grade 16 24 40
Total 30 50 80
If one of these 80 students is selected at random, what is the probability that the student chose Music?
- A. 3/8
- B. 5/8Correct
- C. 12/25
- D. 13/20
Answer: B. 5/8
A total of 50 of the 80 students chose Music, so the probability is 50/80 = 5/8. Choice A is 30/80 = 3/8, the probability of choosing Art rather than Music. Choice C is 24/50, which uses only the tenth-grade Music students over all Music students (the wrong denominator). Choice D is 26/40 = 13/20, which restricts to ninth graders only instead of using all 80 students.
Why the other answers are wrong
- A. 3/8
- That's 30/80, the probability of choosing Art; the Music total is 50, so the probability is 50/80.
- C. 12/25
- That's 24/50, the tenth-grade Music students out of all Music students. Since the student is chosen from all 80 students, the denominator must be 80.
- D. 13/20
- That's 26/40, which uses only ninth graders; the student is selected from all 80 students, so use 50/80.
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