Question
If you flip a coin 8 times, what is the probability for every flip to be heads.
Answers
GPT-4o mini
The probability of getting heads on a single flip of a fair coin is \( \frac{1}{2} \). When flipping the coin multiple times, the flips are independent events, so the probability of getting heads on all 8 flips is calculated by multiplying the probability of heads for each flip.
Thus, the probability \( P \) of getting heads on all 8 flips is given by:
\[
P = \left( \frac{1}{2} \right)^8
\]
Calculating this:
\[
P = \frac{1}{2^8} = \frac{1}{256}
\]
Therefore, the probability of flipping heads on all 8 flips is \( \frac{1}{256} \).
Thus, the probability \( P \) of getting heads on all 8 flips is given by:
\[
P = \left( \frac{1}{2} \right)^8
\]
Calculating this:
\[
P = \frac{1}{2^8} = \frac{1}{256}
\]
Therefore, the probability of flipping heads on all 8 flips is \( \frac{1}{256} \).