Dirk Nowitzki of the Dallas Mavericks has a 87.7% career free throw record. Assuming that free throws represent independent events, find the probability of Nowitzki
a. Getting 3 free shots in a row
b. Missing exactly one of 3 free shots
pr(3 makes)=.877^3
pr(missingone)= 3*.123*.87^2
To find the probability of certain events happening, we can use the concept of independent events. This means that the outcome of one event does not affect the outcome of the other.
The probability of Nowitzki making a free throw is given as 87.7% or 0.877, and the probability of missing a free throw is 1 - 0.877 = 0.123.
a. Finding the probability of Nowitzki making 3 free throws in a row:
Since the events are independent, we can multiply the probabilities of each event happening. So, the probability of making the first free throw is 0.877, the second free throw is also 0.877, and the third free throw is again 0.877.
Therefore, the probability of making 3 free throws in a row is:
0.877 * 0.877 * 0.877 = 0.688
b. Finding the probability of Nowitzki missing exactly one of three free shots:
There are three possible scenarios where Nowitzki can miss exactly one free throw: miss the first and make the next two, make the first and miss the next two, or make the first two and miss the last one.
The probability of missing a free throw is 0.123, and the probability of making a free throw is 0.877. Therefore, we can calculate the probability for each scenario and add them together.
1. Miss first and make next two: 0.123 * 0.877 * 0.877 = 0.094
2. Make first and miss next two: 0.877 * 0.123 * 0.877 = 0.094
3. Make first two and miss last one: 0.877 * 0.877 * 0.123 = 0.094
Adding these probabilities together: 0.094 + 0.094 + 0.094 = 0.282
Therefore, the probability of Nowitzki missing exactly one of three free shots is 0.282.