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