A college basketball player who sinks 75% of her free throws comes to the line t

Question

A college basketball player who sinks 75% of her free throws comes to the line to shoot a "one and one" (if the first shot is successful, she is allowed a second shot, but no second shot is taken if the first is missed; one point is scored for each successful shot). Assume that the outcome of the second shot, if any, is independent of that of the first. Find the expected number of points resulting from the "one and one." Compare this with the expected number of points from a "two-shot foul," where a second shot is allowed, irrespective of the outcome of the first.

Explanation / Answer

"one and one" situation: P(0)=25% P(2)=0.75*0.75=56.25% P(1)=0.75*0.25=18.75% E=0*0.25+1*0.1875+2*0.5625=1.3125 points. "two shot-foul" P(0)=0.25*0.25=6.25% P(2)=56.25% P(1)=37.5% E=1*0.375+2*0.5625=1.5 points

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