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John 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
35
35% free throw shooter what is the percent chance that John makes all three free throws? Do not round your answer

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1 answer

To find the probability that John makes all three free throws, we can use the fact that each free throw is an independent event. The probability of making a single free throw is 35%, which can be expressed as a decimal:

\[ P(\text{make one free throw}) = 0.35 \]

Since the free throws are independent, we multiply the probabilities of making each free throw together:

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

This becomes:

\[ P(\text{make all three free throws}) = 0.35 \times 0.35 \times 0.35 \]

Calculating this gives:

\[ P(\text{make all three free throws}) = 0.35^3 \]

Calculating \(0.35^3\):

\[ 0.35^3 = 0.042875 \]

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

\[ 0.042875 \times 100 = 4.2875 \]

Thus, the percent chance that John makes all three free throws is:

\[ \boxed{4.2875} \]