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S1 Help

A golfer has 5 different clubs ina golf bag, only one of which is correct for the shot about to be played. The probability that the golfer plays a good shot if the correct club is chosen is 1/3. The probability of a good shot with an incorrect club is 1/4. The golfer chooses a club at random and plays the shot. Find the probability that;

a) a good shot is made
b) an incorrect club was used, given that a good shot is played

Thank you in advance for any help anybody an give me

Reply 1

Tut
A golfer has 5 different clubs ina golf bag, only one of which is correct for the shot about to be played. The probability that the golfer plays a good shot if the correct club is chosen is 1/3. The probability of a good shot with an incorrect club is 1/4. The golfer chooses a club at random and plays the shot. Find the probability that;

a) a good shot is made
b) an incorrect club was used, given that a good shot is played

Thank you in advance for any help anybody an give me


G = Good shot
C = umm.. :smile:.. 'Not Good' shot
W = Wrong club
R = Right club

a.) P(G) = P(WnG) + P(RnG)

wrong club and good shot = (4/5)(1/4) = 1/5
right club and good shot = (1/5)(1/3) = 1/15

P(G) = 1/5 + 1/15 = 4/15

b.) P(W|G) = P(WnG)/P(G) = (1/5)(4/15) = 3/4