Random Selection of Answers on a Multiple-choice Test.

Beth is taking a ten-question multiple-choice test for which each question has three answer choices, only one of which is correct. Beth decides on answers by rolling a fair die and marking the first answer choice if the die shows 1 or 2, the second if it shows 3 or 4, and the third if it shows 5 or 6. Find the probability of each event.

(a) exactly four correct answers

(b) fewer than three correct answers