Question

Let's say that you play basketball very well and you are at the free throw line 10 times during the Crown Invitational Basketball Tournament. The chance of you making a free throw is 90% based on the data from a full season of basketball games. If you shoot 10 free throws during this game...

1. What is the probability that you make exactly 9 shots? (we will assume all ten are independent from one another)

2. What is the probability that you make at least 9 shots? (we will assume at ten are independent from one another)

3. Is this what you expected? Any surprises?

Answer 1

1)
Here, n = 10, p = 0.9, (1 - p) = 0.1 and x = 9
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 9)
P(X = 9) = 10C9 * 0.9^9 * 0.1^1
P(X = 9) = 0.3874

2)

Here, n = 10, p = 0.9, (1 - p) = 0.1 and x = 9
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X >= 9).
P(X >= 9) = (10C9 * 0.9^9 * 0.1^1) + (10C10 * 0.9^10 * 0.1^0)
P(X >= 9) = 0.3874 + 0.3487
P(X >= 9) = 0.7361

3)

mena = np
= 10 * 0.9
= 9