On a certain hole, a golfer knows that he has a 70 percent chance of reaching the green (putting surface) in one stroke, 20 percent in two strokes, 8 percent in three, and 2 percent in four or more. If he reaches the green on his first stroke, he has an 80 percent chance of putting the golf ball in the cup on his second stroke. If he does not reach the green on his first stroke, then he has a 30 percent chance of putting the golf ball in the cup on his second stroke. What is the probability that the golfer will reach the green in one stroke and put the ball in the cup on his second stroke?
The chance of reaching the green on the first stroke is 70%, or 0.70. Given that he reaches it, the chance of sinking the ball on the second stroke is 80%, or 0.80. Multiply these probabilities: 0.70 × 0.80 = 0.56, so the probability is 0.56, choice B.
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