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.
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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!