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if the probability that a certain tennis player will serve an ace is 1 4 , what is the probability that he will serve exactly four aces out of seven serves? (assume that the seven serves are independent. round your answer to four decimal places.)

Sagot :

The probability that he will serve exactly four aces out of seven serves is 5.7 %.

Given :

if the probability that a certain tennis player will serve an ace is 1 / 4 .

If we let p stand for the probability of a succes, then p = 1/4, and ( 1 - p ) = 3/4.  (1-p) is the probability that he will NOT serve an ace.

Formula  for probability:

P (m successes in n trials) = ( nCm ) * p^m * ( 1 - p )^( n - m ).

= 7C4 * ( 1/4 )^4 * ( 3/4 )^( 7 - 4 )

= 7! / ( 7 - 4 )! 4! * 1/256 * 27/64

= 7 * 6 * 5 / 3 * 2 * 1 / 256 * 27/64

= 35/256 * 27/64

= 945/16384

= 0.057

= 0.057 * 100 %

= 5.7 %

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