If the probability that a certain tennis player will serve an ace is 0.2, what is the probability that he will serve at least three aces out of five serves?
A) 0.0512
B) 0.6656
C) 0.0067
D) 0.0579

Question

Quizplus · Accepted Answer

The probability of serving at least three aces out of five serves can be calculated using the binomial probability formula, which is P(X = k) = C(n, k) * p^k * (1-p)^(n-k), where C(n, k) is the combination of n items taken k at a time, p is the probability of success (serving an ace in this case), and n is the total number of trials (serves). To find the probability of serving at least three aces, we calculate the probability of serving exactly three aces, exactly four aces, and exactly five aces, and then sum these probabilities.P(3 aces) = C(5, 3) * (0.2)^3 * (0.8)^2P(4 aces) = C(5, 4) * (0.2)^4 * (0.8)^1P(5 aces) = C(5, 5) * (0.2)^5 * (0.8)^0Summing these probabilities gives the total probability of serving at least three aces out of five serves, which is 0.05792, rounded to 0.0579.

If the Probability That a Certain Tennis Player Will Serve