What is the probability of tossing a coin 5 times and each time getting heads

Question

What is the probability of tossing a coin 5 times and each time getting heads

Answer 1

(1/2)^5 = 1/2^5 = 1/32

1/32 = 3.125% chance of 5 heads in 5 flips

probability of one head in one flip = 1/2

probability of 5 heads in 5 flips = 1/2 x 1/2 x 1/2 x 1/2 x 1/2 = 1/32

this assumes a fair coin. also the coin has "no memory" if it flips 4 heads, that doesn't change the probability of the 5th flip's probability.

However, it is evidence you may have an unfair coin. It it comes up heads 5 times, you may to look and see if it's a two headed coin.

Actually, coins seem to be slightly heavier on the head side, so may expect slightly more than 50% it will turn up heads.

Answer 2

Raymond is correct!

Just to expand on his answer a bit, if we're talking about independent events, then all you need to do is multiply the probability of the outcome by itself as many times as there are trials, or put differently, it's the probability of the outcome (in this case, 1/2) to the n-th power, where n is the number of trials (in this case, 5).

So in this case, the probability of getting heads on a fair coin flip is 1/2 and we want the probability of getting heads five times, so that's

(1/2)^5

or

1/2 x 1/2 x 1/2 x 1/2 x 1/2

which equals 1/32, as he said above.

Hope that helps!