Give stream of consciousness and then the final answer. An archer is shooting arrows from various distances. She shoots at a target from 40 yards, 50 yards, and 60 yards. The probability that she hits within the bullseye from 40 yards is 4/5, the probability that she hits within the bullseye from 50 yards is 3/4, and the probability that she hits within the bullseye from 60 yards is 2/3. What is the probability that she hits the bullseye at least once in three shots, one from each distance listed.
Options:
(A) 39/40
(B) 49/50
(C) 59/60
(D) 9/10
(E) 14/15
The probability that she hits the bullseye at least once = 1 - (the probability that she misses the bullseye every shot)
The probability that she misses every shot = (prob that she misses from 40 yards)*(prob that she misses from 50 yards)*(prob that she misses from 60 yards)
Prob that she misses from 40 yards = 1 - 4/5 = 1/5; Prob that she misses from 50 yards = 1 - 3/4 = 1/4; Prob that she misses from 60 yards = 1 - 2/3 = 1/3
Thus the probability that she misses all shots = (1/5)*(1/4)*(1/3) = 1/60
Thus the probability that she makes at least one shot = 1 - (1/60) = 59/60
The final answer: (C).