Problem-Solving and Data AnalysisMediumTwo-way tables
Problem-Solving and Data Analysis practice question
A survey of 200 people recorded their favorite drink by age group:
Coffee Tea Total
Under 30 40 60 100
30 and over 70 30 100
Total 110 90 200
If one person is chosen at random from those who prefer tea, what is the probability the person is under 30?
- A. 60/200
- B. 60/100
- C. 60/90Correct
- D. 90/200
Answer: C. 60/90
The condition 'from those who prefer tea' restricts the sample space to the 90 tea drinkers. Of those, 60 are under 30, so the probability is 60/90. The trap is using the full total 200 (choice A) instead of the conditional total.
Why the other answers are wrong
- A. 60/200
- You used the full survey total of 200 as the denominator, but 'chosen from those who prefer tea' restricts the group to the 90 tea drinkers.
- B. 60/100
- You divided by the 100 people under 30, which answers the reverse question (given under 30, probability of tea); here the given group is tea drinkers, so the denominator is 90.
- D. 90/200
- 90/200 is the probability that a random person prefers tea, not the probability of being under 30 among tea drinkers — that's 60 out of 90.
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