Question

Describe the likelihood of the following statement.
You flip a fair coin and get 50 heads in a row.
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Part 1
What best describes the likelihood of the​ statement?

Answer 1

To assess the likelihood of flipping a fair coin and getting 50 heads in a row, we can analyze the probability associated with this event.

1. **Probability of a single coin flip**: A fair coin has two possible outcomes: heads (H) or tails (T). The probability of getting heads in a single flip is 1/2.

2. **Probability of multiple flips**: The probability of getting heads in multiple flips is calculated by raising the probability of a single flip to the power of the number of flips. For 50 heads in a row, the calculation is:

\[
P(\text{50 heads}) = \left( \frac{1}{2} \right)^{50}
\]

This equates to:

\[
P(\text{50 heads}) = \frac{1}{2^{50}} \approx 1.12 \times 10^{-15}
\]

3. **Interpreting the probability**: The resulting probability of obtaining 50 heads in a row (approximately \(1.12 \times 10^{-15}\)) is an extremely small number. This suggests that while it is technically possible, it is extraordinarily unlikely to happen.

### Conclusion:
The likelihood of flipping a fair coin and getting 50 heads in a row is extremely low (or negligible), making it highly improbable to occur in any reasonable scenario.