The probability that a given computer chip will fail is 0.02. find the probability that of 5 delivered chips, exactly 2 will fail.

Since the chip either passes or fails, this problem is one in binomial probability, with p(fail)=0.02 and n=5.
                 
If your calculator features probability functions such as binompdf(n, p), use it.
Mine is a TI-83 Plus.

The probability that exactly two chips will fail is

binompdf(5,0.02,2) = 0.0038.  This is quite a small probability.