ohn has to make all 3 free throws to win the game. Assume each free throw is an independent event and that the pressure of the situation has no impact on him. If John is a

80
80% free throw shooter what is the percent chance that John makes all three free throws? Do not round your answer.

1 answer

To find the probability that John makes all three free throws, we can use the multiplication rule for independent events.

Since John's free throw shooting percentage is 80%, we can express this as a decimal:

\[ P(\text{make a free throw}) = 0.80 \]

Since each free throw is an independent event, we can multiply the probabilities of making each individual free throw together:

\[ P(\text{making all three free throws}) = P(\text{make first}) \times P(\text{make second}) \times P(\text{make third}) \]

This can be calculated as:

\[ P(\text{making all three free throws}) = 0.80 \times 0.80 \times 0.80 = 0.80^3 \]

Now we calculate \(0.80^3\):

\[ 0.80^3 = 0.512 \]

To express this as a percentage, we multiply by 100:

\[ 0.512 \times 100 = 51.2% \]

Therefore, the percent chance that John makes all three free throws is 51.2%.