Question

1) A very short quiz has one multiple choice question with five possible choices (a, b, c, d, e) and one true or false question. Assume you are taking the quiz but do not have any idea what the correct answer is to either question, but you mark an answer anyway. What is the probability you have given the correct answer to the multiple choice question? Enter your answer as a decimal rounded to two decimal places. (Hint: Use a tree diagram to help you with this problem.)

2) Refer to question 1. What is the probability that you have given the correct answer to the true or false question? Enter your answer as a decimal rounded to two decimal places.

3) Refer to question 1. What is the probability that you have given the correct answer for both of the questions?  Enter your answer as a decimal rounded to two decimal places.

4) Refer to question 1. What is the probability that you have given the correct answer to at least one of the questions?  Enter your answer as a decimal rounded to two decimal places.

5)Refer to question 1. What is the probability that you have given the incorrect answer to both questions?  Enter your answer as a decimal rounded to two decimal places.

Answer 1

1) For the first question there are five options

So probability of selecting correct option is

2) For the second question, there are two options

So probability of selecting correct option is

3) As giving correct answer to any one is independent of the other.

Hence, the required probability is

4) Probability of answering at least one is

5) Giving incorrect answer to both questions is the complement of the event of answering at least one is

Hence the probability is