Teresa, a star player in women's college softball, is participating in a home run contest. If the probability she will hit a home run on any pitch is 0.65 what is the probability that out of 10 tries, at least 7 will be home runs?
A) 0.5139
B) 0.0260
C) 0.0719
D) 0.6496

Question

Quizplus · Accepted Answer

We can use the binomial probability formula to solve this problem:

P(X ≥ 7) = 1 - P(X ≤ 6)

Where X is the number of home runs hit out of 10 pitches.

Using the formula for binomial probability, we can find P(X ≤ 6) as follows:

P(X ≤ 6) = Σ(i=0 to 6) C(10,i) * (0.65)^i * (1-0.65)^(10-i)

Where C(10,i) represents the number of ways to choose i successful pitches out of 10, and (0.65)^i * (1-0.65)^(10-i) represents the probability of getting i successful pitches and 10-i unsuccessful pitches.

Using a calculator, we find that P(X ≤ 6) ≈ 0.4861.

Therefore, P(X ≥ 7) = 1 - P(X ≤ 6) ≈ 1 - 0.4861 = 0.5139.

Thus, the best choice is A.

Teresa, a Star Player in Women's College Softball, Is Participating