The probability for an archer hitting a target

The probability for an archer hitting a target is 10%. If he shoots ten times independently what is the probability that the target will be hit atleast once?

The probability of hitting the target at least once is

1 - P(never hitting target in 10 shots) = 1 - (0.9)^10 = 0.651 or about 65%.

Note that the probability of not hitting the target on any given shot is

1 - 0.1 = 0.9.

P(hitting at least once) = 1 - P(missing all 10 times)

P(missing all 10 times) = (0.9)^10