SIG (Susquehanna)–styleTraderJunior TraderQuestion #116
You have two torpedoes to hit a boat. Each torpedo has a 2/3 chance of hitting the boat. If you launch both torpedoes, what is the probability that the boat is hit?
Free worked solution · Quant Blueprint
8/9 if the two torpedoes hit independently; marginal hit probabilities alone are insufficient.
- The boat is missed by both only if both torpedoes miss. Each miss probability is 1/3.
- Under independence, P(both miss) = (1/3)² = 1/9.
- Take the complement: P(at least one hit) = 1 − 1/9 = 8/9.
Common mistake
Adding 2/3 + 2/3 double-counts the event where both hit and even exceeds one. Independence must be stated; a shared cause can correlate the attempts.
Follow-up
Without independence, P(at least one hit) = 4/3 − P(both hit). Given only the marginals, its possible range is 2/3 to 1.
Original educational explanation for this practice question. Reviewed . Firm-style practice; the label describes the collection’s preparation context.
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