Final answer:
To find the probability of all 6 serves being successful, we can use the binomial probability formula. Plugging in the values, we get a probability of 12.01%.
Step-by-step explanation:
To find the probabilities, we need to use the binomial probability formula. Let's denote a successful first serve as 'S' and an unsuccessful first serve as 'U'. The probability of a successful first serve (S) is 0.62, and the probability of an unsuccessful first serve (U) is 0.38. Since each serve is independent of the others, we can use the binomial probability formula:
P(X = k) = C(n, k) * p^k * (1-p)^(n-k)
where n is the total number of serves, k is the number of successful serves (in this case, all successful serves), and p is the probability of a successful serve. Plugging in the values, we get:
P(X = 6) = C(6, 6) * 0.62^6 * (1-0.62)^(6-6)
P(X = 6) = 1 * 0.62^6 * 0.38^0
P(X = 6) = 0.62^6 * 1
P(X = 6) = 0.1201
Therefore, the probability of all 6 serves being successful is 0.1201 or 12.01%.