Question
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 (Round to five decimal places as needed.)
Ask by Wang Haynes. in the United States
Mar 09,2025
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Tutor-Verified Answer
Answer
The probability of getting seven heads in a row when flipping a coin is 0.00781.
Solution
1. When flipping a coin, the probability of getting a head on one flip is \( \frac{1}{2} \).
2. Since the coin flips are independent, the probability of getting seven heads in a row is computed as:
\[
\left(\frac{1}{2}\right)^7 = \frac{1}{128}
\]
3. Numerically, \(\frac{1}{128} \approx 0.00781\) when rounded to five decimal places.
4. This probability means that if you flip a coin repeatedly, on average, only about 0.78% of the sequences of 7 consecutive flips will all be heads.
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Simplify this solution The Deep Dive
The probability of obtaining heads on a fair coin flip is 0.5. Therefore, to find the probability of getting seven heads in a row, you would calculate \(0.5^7\), which equals approximately 0.00781 when rounded to five decimal places. This means there's a very slim chance—about 0.781%—of flipping seven heads in a row. This probability highlights the surprising nature of sequences in probability. While it may seem that getting heads repeatedly is common, the reality is that each flip is independent, and this independence means that such long sequences become increasingly unlikely. So, don’t be surprised if your coin doesn’t cooperate!
