Question

A five-question quiz is taken in which the first and second questions have four answer choices, the third and fourth questions have three answer choices, and the last question has five answer choices. If a student randomly marks an answer for each question, what is the expected number of questions he will answer correctly?

Answer 1

The expected number of questions the student will answer correctly can be found by calculating the probabilities of getting each question correct and multiplying them by the number of questions. The expected number is 41/30.

Step-by-step explanation:

The expected number of questions the student will answer correctly can be found by multiplying the probability of getting each question correct by the number of questions. Let's calculate it step by step:

1. The first two questions have 4 answer choices each, so the probability of getting each question correct is 1/4. Therefore, the expected number of correct answers for these two questions is 2 * (1/4) = 1/2.
2. The next two questions have 3 answer choices each, so the probability of getting each question correct is 1/3. Therefore, the expected number of correct answers for these two questions is 2 * (1/3) = 2/3.
3. The last question has 5 answer choices, so the probability of getting it correct is 1/5. Therefore, the expected number of correct answers for the last question is 1 * (1/5) = 1/5.

Now we can sum up the expected number of correct answers for all the questions: 1/2 + 2/3 + 1/5 = 15/30 + 20/30 + 6/30 = 41/30.

Therefore, the expected number of questions the student will answer correctly is 41/30.

Answer 2

1.37

Step-by-step explanation: