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What is the probability of obtaining seven heads in a row when flipping a coin? Interpret this probability. The probability of obtaining seven heads in a row when flipping a coin is 0.00781 . (Round to five decimal places as needed.) Interpret this probability. Consider the event of a coin being flipped seven times. If that event is repeated ten thousand different times, it is expected that the event would result in seven heads about \( \square \) time(s). (Round to the nearest whole number as needed.)

Ask by Ruiz Haynes. in the United States
Mar 09,2025

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The probability of getting seven heads in a row when flipping a coin is 0.00781. If the coin is flipped seven times 10,000 times, it is expected to result in seven heads about 78 times.

Solución

The probability of getting seven heads in a row is computed as follows: 1. Each coin flip has a probability of \( \frac{1}{2} \) for heads. For seven flips, the probability is \[ \left(\frac{1}{2}\right)^7 = \frac{1}{128} \approx 0.00781. \] 2. If the event (flipping a coin seven times) is repeated \( 10,\!000 \) times, then the expected number of times to obtain seven heads in a row is \[ 10,\!000 \times 0.00781 \approx 78.125. \] Rounding to the nearest whole number gives \( 78 \). Thus, if the event is repeated \( 10,\!000 \) times, it is expected to result in seven heads about \( \boxed{78} \) times.

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Mind Expander

When you flip a fair coin, the chance of getting heads in a single flip is 0.5. For seven consecutive heads, the probability is \( 0.5^7 \), which gives us approximately 0.00781. This means if you attempted this experiment 10,000 times, you would expect to get seven heads in a row roughly 78 times. So, while it is certainly possible, it’s a relatively rare outcome! If you're brainstorming ideas to improve your chances, consider how the concept of streaks applies in games of chance. However, remember that each flip is independent. You might often encounter streaks, but they don’t change the underlying probabilities! Stay aware of confirmation bias—thinking a pattern exists when it’s just random flips at play.

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