a tennis player is satisfied with his game if more than 70 p

a tennis player is satisfied with his game if more than 70 percent of his first serves are good. on clay courst, the probability that his first serve is good is .8. on grass the probability is .7. assume indivisual serves are independent

A) if he is playing on clay tomorrow and has 20 first serves, find the probability that he will be satisfied.

B) if he is playing on grass tomorrow and has 20 first serves, find the probability that he will be satisfied.

C) if the probability is .6 that he will play on clay and .4 on grass, find the probability he will be satisfied if he has 20 first serves.

Solution

a) the probability that he will be satisfied.= prob that his serves are good is >70%

prob services are good = 20(0.8)/20=0.80 Hence prob he will be satisfied = 1

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B)_prob for his success = 20(0.7)/20 = 0.70

His prob for being satified =1

c) prob for success = 0.6(0.8) + (0.4)(0.7) = 0.76

He will be satisfied.