If a student answers questions on a true-false test randomly (i.e., assume that p = 0.5) and independently, determine the probability that:

a) the first correct answer is in response to question 4

b) at most four questions (that is, four or fewer) must be answered to get the first correct answer.

Please explain why you would use binomial distribution or negative binomial distribution for this problem (instead of the other). Thank you!