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) No, If Amy makes a free draw, Bob does not make.

b) Yes, The probability of a player making a free throw does not depend on the subsequent games

c) The probability that Amy makes her free three of three free throws is given by;

3/4 X 3/4 X 3/4

=27/64

The probability that Bob does not make any of her free throws is given by

1/3 x 1/3 x 1/3

=1/27

d) The probability that Bob makes three of three free throws is given by

2/3 x 2/3 x 2/3

=8/27

The probability that Amy does not make three free throws in three games is

1/4 x 1/4 x 1/4

= 1/64

e) If both Amy and Bob take three free throws, the probability that the margin is three is given by the difference of the probabilities that both of the takes three free throws

27/64 - 8/27

= 217/1728

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