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3. Your friend makes a free throw \( 50 \% \) of the time. Your friend attempts four free throws, You design and perform a simulation that involves tossing four coins. Heads \( (H) \) represents making the free throw, and tails \( (T) \) represents not making the free throw.

Ask by Ford Thornton. in the United States
Mar 14,2025

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When your friend attempts four free throws with a 50% chance of making each, the probability of making exactly \( k \) free throws is calculated using the binomial formula. Here are the probabilities for each possible number of successful free throws: - 0 made: 6.25% - 1 made: 25% - 2 made: 37.5% - 3 made: 25% - 4 made: 6.25% These probabilities are based on tossing four coins, where heads represent a made free throw and tails represent a missed one.

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Bonus Knowledge

Did you know that the concept of using coin tosses to simulate probabilities can be traced back to early statistics and games of chance? This fun method highlights the essence of random events and is a great way to visualize outcomes, especially when dealing with a \( 50\% \) chance. By tossing four coins, you're effectively simulating your friend's free throw attempts, making it more relatable and engaging—who doesn't love a little coin tossing fun? In practical terms, you can enhance your simulation by recording the results of multiple sets of four tosses. By tracking how many heads (successful free throws) appear in each trial, you can calculate empirical probabilities and even visualize them with charts or graphs. This can illustrate the law of large numbers, wherein as you perform more simulations, the results will get closer to the expected \( 50\% \) success rate, making your exploration both educational and exciting!

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