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Statistics · Question of the Day

Statistics Question of the Day

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Monday, August 24, 2026

In a student survey, event AA is that a randomly selected student plays a school sport and event BB is that the student is in the school band. The probabilities are P(A)=0.40P(A)=0.40, P(B)=0.35P(B)=0.35, and P(A∩B)=0.15P(A\cap B)=0.15. What is the probability that AA or BB occurs (inclusive or: sport, band, or both)?

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Question of the Day

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In a student survey, event AA is that a randomly selected student plays a school sport and event BB is that the student is in the school band. The probabilities are P(A)=0.40P(A)=0.40, P(B)=0.35P(B)=0.35, and P(A∩B)=0.15P(A\cap B)=0.15. What is the probability that AA or BB occurs (inclusive or: sport, band, or both)?

  1. 0.60 (correct answer)
  2. 0.75
  3. 0.45
  4. 0.15

Explanation: This question tests the Addition Rule for probability, which finds P(A or B) when events can overlap. Simply adding P(A) = 0.40 and P(B) = 0.35 gives 0.75, but this double-counts students who do both activities. We must subtract P(A∩B) = 0.15 to correct for this overlap. The calculation is P(A∪B) = P(A) + P(B) - P(A∩B) = 0.40 + 0.35 - 0.15 = 0.60. This gives us the probability that a student plays a sport, is in band, or does both. A common mistake is forgetting to subtract the intersection, which would incorrectly give 0.75. To avoid this error, visualize a Venn diagram where the overlapping region represents students doing both activities.