You toss a fair coin 8 times, what is the probability that you get all heads?
The probability of getting a head on a fair coin is 0.5. For each toss, the probability is independent of previous tosses.
To get all heads in 8 tosses, we need to have a head on each individual toss.
The probability of getting a head on the first toss is 0.5.
The probability of getting a head on the second toss is also 0.5.
Similarly, the probability of getting a head on each of the 8 tosses is 0.5.
Since the tosses are independent, we can multiply the probabilities together:
P(all heads) = P(H on first toss) * P(H on second toss) * ... * P(H on eighth toss)
= 0.5 * 0.5 * 0.5 * 0.5 * 0.5 * 0.5 * 0.5 * 0.5
= 0.5^8
= 0.00390625
Therefore, the probability of getting all heads in 8 tosses of a fair coin is 0.00390625, or approximately 0.39%.