Problem-Solving and Data AnalysisVery hardProbability of independent events all occurring
Problem-Solving and Data Analysis practice question
In a certain game, the probability that a player wins any single round is 0.2, and rounds are independent of one another. What is the probability that a player wins three rounds in a row?
Answer: 0.008 or .008 or 1/125
Independent events: multiply the probabilities. 0.2 × 0.2 × 0.2 = 0.008 (that is, 1/125).
Common wrong answers
- If you answered 0.6
- 0.6 ADDS the three probabilities. Adding is for 'either/or' of events that can't both happen; 'all three' multiplies.
- If you answered 0.2
- 0.2 is the probability of winning ONE round. Three wins in a row is much less likely.
- If you answered 0.06
- 0.06 is 0.2 × 0.3 or 0.2 × 0.2 with a slip; 0.2 × 0.2 × 0.2 = 0.008.
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