During his NBA career Dirk Nowitzki made approximately 90% of all free throw. Suppose Dirk makes 10 free throws in a row. Assuming each free throw is independent, what is the probability he will make the next free throw?
still 90%
To find the probability that Dirk will make the next free throw after making 10 in a row, we can use the concept of independent events. The probability of making each free throw is given as 90% or 0.9.
Since each free throw is independent, the probability of making 10 free throws in a row is (0.9)^10. This is because to calculate the probability of multiple independent events occurring, we multiply their individual probabilities together.
So, the probability that Dirk will make the next free throw after making 10 in a row is (0.9)^10.
Calculating this probability:
(0.9)^10 ≈ 0.3487
Therefore, the probability that Dirk will make the next free throw is approximately 0.3487 or 34.87%.
To calculate the probability that Dirk Nowitzki will make the next free throw, we can use the concept of conditional probability. Given that Dirk has made 10 free throws in a row, the probability of making the next free throw can be calculated as follows:
1. First, we need to determine the probability of making a single free throw. Given that he has made approximately 90% of all free throws during his career, the probability of making a single free throw is 0.90 or 90%.
2. Assuming that each free throw is independent, the probability of making 10 free throws in a row is calculated by multiplying the probability of making each individual free throw together.
P(10 consecutive free throws) = P(make first free throw) * P(make second free throw) * ... * P(make tenth free throw)
P(10 consecutive free throws) = 0.90 * 0.90 * ... * 0.90 (10 times)
This equation represents the probability of making 10 consecutive free throws.
3. Knowing that Dirk has already made 10 free throws in a row, the probability he will make the next free throw can be determined by using conditional probability. This can be done by dividing the probability of making 10 consecutive free throws by the probability of making 10 or more free throws in a row.
P(make next free throw | making 10 free throws in a row) = P(10 consecutive free throws) / P(make 10 or more free throws in a row)
Since we are not given any information about Dirk's previous performance beyond the 10 made free throws, we assume that he would always have a 90% probability of making free throws consistently.
P(make 10 or more free throws in a row) = P(10 consecutive free throws)
Therefore, the probability of making the next free throw is:
P(make next free throw | making 10 free throws in a row) = (0.90 * 0.90 * ... * 0.90) / (0.90 * 0.90 * ... * 0.90)
P(make next free throw | making 10 free throws in a row) = 0.90
This means that the probability Dirk will make the next free throw is 90%.