A baseball team us conprised of 7 pro players and 3 amateur players. The provabi

Question

A baseball team us conprised of 7 pro players and 3 amateur players. The provability that a pro player hit the ball is 0.8 while the amateur is 0.4.
What is the probability that the next ball is hit?
If the last ball was hit, what is the probability that the player who hit it was an amateur? A baseball team us conprised of 7 pro players and 3 amateur players. The provability that a pro player hit the ball is 0.8 while the amateur is 0.4.
What is the probability that the next ball is hit?
If the last ball was hit, what is the probability that the player who hit it was an amateur?
What is the probability that the next ball is hit?
If the last ball was hit, what is the probability that the player who hit it was an amateur?

Explanation / Answer

Probability that a pro-player is selected to hit the ball P(P) = 0.7
Probability that an amateur player is selected to hit the ball P(A) = 0.3

P(H|P) = 0.8
P(H|A) = 0.4

Probability that next ball is hit = P(P)*P(H|P) + P(A)*P(H|A) = 0.7*0.8 + 0.3*0.4 = 0.68

If the last ball was hit, what is the probability it was hit by an Amatuer, P(A|H) = P(H|A)*P(A)/(P(H|A)*P(A) + P(H|P)*P(P)) = 0.3*0.4/(0.3*0.4 + 0.7*0.8) = 0.12/0.68 = 0.1765

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