How likely is it to get a 1.25% chance 27 times in 295 tries?

Question

the question above

Answer 1

If you want the exact binomial probability it is ₂₉₅C_{27 *} (.0125)²⁷ * (.9875)²⁶⁸.

Probably more reasonable to use the normal approximation to the binomial with mean = 295 * .0125 and variance  295 * .0125 * .9875.