Problem-Solving and Data AnalysisHardProbability that two cards are not both hearts
Problem-Solving and Data Analysis practice question
A pack of 8 cards contains 3 hearts. Two cards are drawn at random without replacement. What is the probability that the two cards are not both hearts?
Answer: 25/28
P(both hearts) = 3/8 × 2/7 = 3/28, so P(not both) = 25/28.
Common wrong answers
- If you answered 3/28
- 3/28 is the probability that both are hearts.
- If you answered 55/64
- 55/64 treats the draws as with replacement.
- If you answered 5/8
- 5/8 is the probability that the first card is not a heart.
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