Some question: An archer is shooting arrows from various distances. She shoots at a target from 60 yards, 70 yards, and 80 yards. The probability that she hits within the bullseye from 60 yards is 2/3, the probability that she hits within the bullseye from 70 yards is 3/5, and the probability that she hits within the bullseye from 80 yards is 1/2. What is the probability that she hits the bullseye at least once in three shots, one from each distance listed.\nOptions:\n(A) 19/20\n(B) 29/30\n(C) 49/50\n(D) 9/10\n(E) 14/15
Some stream of consciousness:
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The probability that she hits the bullseye at least once = 1 - (the probability that she misses the bullseye every shot)\nThe probability that she misses every shot = (prob that she misses from 60 yards)*(prob that she misses from 70 yards)*(prob that she misses from 80 yards)\nProb that she misses from 60 yards = 1 - 2/3 = 1/3; Prob that she misses from 70 yards = 1 - 3/5 = 2/5; Prob that she misses from 80 yards = 1 - 1/2 = 1/2\nThus the probability that she misses all shots = (1/3)*(2/5)*(1/2) = 2/30 = 1/15\nThus the probability that she makes at least one shot = 1 - (1/15) = 14/15 The answer: (E).
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