A student takes a true-false test consisting of 15 questions. assuming that the student guesses at each question, find the probability that the student answers exactly 13 questions correctly

There are two possible answers two each question T or F so it has 1/2 of a possiblity of succeding

and there are 15 questions so that gives 1/15 but we need 13 questions so 13/15

and because we need all thirteen to be correct we multiply both

so 13/15*1/2

which gives us 13/30