This is a problem I thought of, is this solution right?

What is the probability of getting two questions correct in a row on a 25 question test with 5 answer choices if you circle ones randomly. i.e. 4 and 5 correct, 24 and 25 correct.

Keep in mind that if you try to use multiplication principle, the number of possible selections for the first question is 24 because there is no question 26 after 25.

My solution:

The probability of getting a question right randomly guessing is 1/5.

There are 24 possible ways to pick the first question correct, and only one to pick the second, without overcounting. Thus, there are just 24 ways to answer the two questions.

The probability of getting two questions right is 1/25.

The probability of choosing two questions in a row is 24/300 = 2/25.

Thus the probability is 1/25 * 2/25 * 24 = 48/625???

Pangolin14 Jan 4, 2021