There are three different options to pick in the bag, so the probability of getting a nickel first is 1/3, and then the probability of getting a penny without replacing the nickel is 1/2, as there will be only 2 options remaining after the nickel was picked.
So the final probability is the product of these probabilities:
Probability is given by number of possible outcomes ÷ number of total outcomes
(a) Number of possible outcomes = 5 questions, number of total outcomes = 10 questions
Probability (I answer all 5 problems correctly) = 5/10 = 1/2
(b) Probability (I answer at least 4 of the problems correctly) means I either answer 4 of the problems or all 5 problems correctly = 4/10 + 5/10 = 9/10