Question

A fair coin is tossed five times. What is the probability that it comes up heads at least once?

Please calculate the probability that a fair coin comes up heads at least once when tossed five times.

Answer 1

The probability of getting heads at least once when a fair coin is tossed five times is
`0.96875`, which is the result of subtracting the probability of getting tails in all five tosses
`(0.03125) from 1`.

Step-by-step explanation:

To calculate the probability that it comes up heads at least once when a fair coin is tossed five times, it's easier to first find the probability of the complement event, which is that the coin comes up tails every time. Since the coin is fair, the probability of getting tails on a single toss is
`0.5`.

For five consecutive tosses, we raise this probability to the power of
`5`:

`P(Tails all five times) = (0.5)^5 = 0.03125`
The probability of getting at least one head is then 1 minus the probability of getting tails all five times

`P(At least one head) = 1 - P(Tails all five times) = 1 - 0.03125 = 0.96875`
So, the probability of getting heads at least once in five tosses of a fair coin is
`0.96875 or 96.875%`.