Problem-Solving and Data AnalysisVery hardProbability of belonging to neither group
Problem-Solving and Data Analysis practice question
Of 200 students, 120 play a sport, 80 play in the band, and 50 do both. If one student is chosen at random, what is the probability that the student neither plays a sport nor plays in the band?
Answer: 1/4 or 0.25
Sport or band: 120 + 80 − 50 = 150. Neither: 200 − 150 = 50, so 50/200 = 1/4.
Common wrong answers
- If you answered 0
- 0 assumes everyone does at least one, but 120 + 80 − 50 is only 150.
- If you answered 1/2
- 1/2 forgets to subtract the 50 who do both.
- If you answered 3/4
- 3/4 is the probability of sport or band, not neither.
More Problem-Solving and Data Analysis questions
- Very hard
An item priced at $200 is first marked down by 20%, and then an additional 10% is taken off the reduced price.… - Very hard
A data set of 6 test scores has a mean of 78. After a 7th score is added, the mean rises to 80. What was the 7… - Very hard
If one of the chips that failed inspection is selected at random, what is the probability that it was produced… - Very hard
The regular price of a bicycle at a shop was increased by 25%. Later, during a sale, this increased price was … - Very hard
What is the result when the mean number of pets is subtracted from the median number of pets? - Very hard
What is the value of x?
Not affiliated with the College Board. SAT is a trademark of the College Board.