Amy and Bob are playing basketball. The probability that Amy makes a free throwi

Question

Amy and Bob are playing basketball. The probability that Amy makes a free throwisp= 3/4. The probability that Bob makes a free throw isq= 2/3. The probability of makingany free throw is the same regardless of recent attempts made by either player.(a) (1 point) Is the event that Amy makes her first free throw independent of the event thatBob makes his first free throw?(b) (1 point) Is the event that Amy makes her second free throw independent of the event thatshe makes her first free throw?(c) (3 points) What is the probability that Amy makes three out of three free throws and Bobdoes not make any of his three free throw attempts?(d) (3 points) What is the probability that Bob makes three out of three free throws and Amydoes not make any of her three attempts?(e) (2 points) If they both take three free throws, what is the probability that the margin ofvictory is three?

Explanation / Answer

A) Yes, the event that Amy makes her first free throw is independent of the event that Bob makes his first free throw

B) Yes, the event that Amy makes her second free throw is independent of the event tht she makes her first free throw

C) P(amy makes 3 out of 3 and Bob makes 0 out of 3) = (3/4 x 3/4 x 3/4) x (1/3 x 1/3 x 1/3) = 0.0156

D) P(Bob makes 3 out of 3 and Amy makes 0 out of 3) = (1/4 x 1/4 x 1/4) x (2/3 x 2/3 x 2/3) = 0.0046

E) Probability that margin of victory is 3 = 0.0156 + 0.0046 = 0.0202

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