In a school survey, event is “a randomly selected student plays a sport” and event is “a randomly selected student is in the band.” The survey reports , , and . What is , where “or” is inclusive (sport or band or both)?
- 0.77 (correct answer)
- 0.18
- 0.95
- 0.59
Explanation: This question tests the Addition Rule for finding the probability of the union of two events, P(A ∪ B). Simply adding P(A) and P(B) would double-count the students who both play a sport and are in the band, overestimating the total. Subtracting P(A ∩ B) corrects for this overlap, ensuring each student is counted only once. Using the given values, P(A ∪ B) = 0.55 + 0.40 - 0.18 = 0.77. This correct answer of 0.77 represents the inclusive probability of a student playing a sport or being in the band or both. A common mistake is forgetting to subtract the intersection, which would give 0.95, but that's too high because of the double-counting. To avoid this, mentally sketch a Venn diagram to visualize the overlap and remember to subtract it.