Question

A quick quiz consists of a multiple-choice question with 6 possible answers followed by a multiple-choice question with 5 possible answers. If both questions are answered with random guesses, find the probability that both responses are correct. Report the answer as a percent rounded to two decimal place accuracy. You need not enter the "%" symbol

Answer 1

3.33

Explanation:

Independent events:

If two events, A and B, are independent, we have that:

`P(A \cap B) = P(A)*P(B)`

In this question, we have that:

The question are independent of each other.

Event A: Correct guess on the first question.

Event B: Correct guess on the second question.

A quick quiz consists of a multiple-choice question with 6 possible answers followed by a multiple-choice question with 5 possible answers.

This means that
`P(A) = (1)/(6), P(B) = (1)/(5)`

Probability that both responses are correct.

`P(A \cap B) = (1)/(6)*(1)/(5) = (1)/(30) = 0.333`

The answer is 3.33%. Since it asks without the "%" symbol, 3.33