Question

# Let's say that you play basketball very well and you are at the free throw line...

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?

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