Homework SourseIt is believed that the probablility of serving an ace in te
It is believed that the probablility of serving an ace in tennis on any given serve is 0.2. If a tennis player serves 8 times, what is the probablility that he makes an ace on at least 2 of the 8 serves?
It is believed that the probablility of serving an ace in tennis on any given serve is 0.2. If a tennis player serves 8 times, what is the probablility that he makes an ace on at least 2 of the 8 serves?
Solution
Binomial Distribution
PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial
P( X < 2) = P(X=1) + P(X=0)
= ( 8 1 ) * 0.2^1 * ( 1- 0.2 ) ^7 + ( 8 0 ) * 0.2^0 * ( 1- 0.2 ) ^8
= 0.5033
P( X > = 2 ) = 1 - P( X < 2) = 0.4967
