As you follow your favorite NBA basketball team’s statistics, you notice the point guard is successfully shooting 85% from the free-throw line for this season. Assuming he is fouled near the end of a game and shoots with that same success rate, what is the probability that he will make at least one free throw when given two chances? Show your work that you used to arrive at your conclusion.
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
P(1) = .85 * .15 = ?
P(2) = .85 * .85 = ?
Either-or probabilities are found by adding the individual probabilities.
12.75%
To calculate the probability of the point guard making at least one free throw when given two chances, we can use the concept of complementary probability.
The probability of making at least one free throw is equal to 1 minus the probability of missing both free throws.
We know that the point guard has a shooting success rate of 85%, which means he makes 85 out of every 100 free throws. Therefore, the probability of making a single free throw is 0.85.
To find the probability of missing a single free throw, we subtract the probability of making a single free throw from 1:
1 - 0.85 = 0.15
Since each free throw attempt is independent, the probability of missing both free throws is the product of the probabilities of missing each individual free throw:
0.15 * 0.15 = 0.0225
Now, we can calculate the probability of making at least one free throw:
1 - 0.0225 = 0.9775
Therefore, the probability that the point guard will make at least one free throw when given two chances is approximately 0.9775, or 97.75%.