The probability that an archer hits a target on a given shot is .7 if five shots are fired find the probability that the archer hits the target on three shots out of the five.

This is a problem in "binomial probability."  Either the archer hits his target or he does not.  This experiment is performed 5 times (so that n=5), and the probability that the archer will hit the target is 0.7 (so that p=0.7).

We need to find the binomial probability that x=3 when the possible outcomes are {0, 1, 2, 3, 4, 5}.

You could use a table of binomial probabilities to evaluate the following:

P(5, 0.7, 3).

Alternatively, you could use a TI-83 or TI-84 calculator and its built-in "binompdf(  " function.

I evaluated binompdf(5,0.7,3) and obtained the result 0.309.