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Solve. N. Kareem stepped to the free throw line fo two shots. If the probability of making each shot is \( \frac{3}{4} \), what is the probability that he will make both shots?

Ask by Gross Murray. in the United States
Jan 29,2025

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The probability that N. Kareem makes both shots is \( \frac{9}{16} \).

Solución

To determine the probability that N. Kareem makes both free throw shots, we'll follow these steps: 1. **Understand the Probability for One Shot:** - The probability of making a single free throw is \( \frac{3}{4} \). 2. **Assume Independence:** - We'll assume that each shot is independent of the other. This means the outcome of the first shot does not affect the outcome of the second shot. 3. **Calculate the Combined Probability:** - To find the probability of both independent events occurring together (making both shots), multiply the probabilities of each individual event: \[ \text{Probability of making both shots} = \frac{3}{4} \times \frac{3}{4} = \frac{9}{16} \] **Final Answer:** The probability that N. Kareem makes both shots is \( \frac{9}{16} \).

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Beyond the Answer

To find the probability that N. Kareem makes both free throws, you simply multiply the probability of making the first shot by the probability of making the second shot since the shots are independent events. The probability of making a single shot is \( \frac{3}{4} \). So, the probability of making both shots is: \[ \frac{3}{4} \times \frac{3}{4} = \frac{9}{16} \] Thus, the probability that he will make both shots is \( \frac{9}{16} \).

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