Question

If layne is a 75% free-throw shooter, A)what is the probability that she makes exactly 3 of the 5 shots that she takes in the game?
B) what is the probability that she misses 2 of the 5 shots that she takes in the game?

using the information above about Laynes free-throw shooting ability. Assume that Layne is a 43% 3-point shooter. your team is ahead by 2 points with less than a second on the clock and Layne is about to shoot a 3 point shot that will win the game if she makes it. also assume that if you foul her during the shot she will NOT make the 3 point shot. would you be better off fouling Layne or letting her try to make the 3-point shot? (Use numbers, understand that in order to win the game Layne MUST make ALL 3 of her free-throw shots)

Answer 1

a) probability that she makes exactly 3 of the 5 shots that she takes in the game =⁵C₃(0.75)³(0.25)² =0.2637

b)

probability that she misses 2 of the 5 shots that she takes in the game =P( she makes exactly 3 of the 5 shots that she takes in the game)=0.2637

c)

for if foul made; probability of making all three free shots =³C₃(0.75)³(0.25)² =0.4219

as this is less than making a 3-point shoot .

therefore one is better off fouling Layne or letting her try to make the 3-point shot