Question

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.
a. What is the probability that you have given the correct answer to both questions?
b. What is the probability that only one of the two answers is correct?
c. What is the probability that neither answer is correct?
d. What is the probability that only your answer to the multiple-choice question is correct?
e. What is the probability that you have only answered the true or false question correctly?

Answer 1

a. The probability that both questions are answered

correctly   = 0.1

b. The probability that only one  questions is

answered correctly  = 0.5

c. The probability that none questions is

answered correctly  = 0.4

d. The probability that only question 1 is

answered correctly   = 0.1

e. The probability that only question 2 is answered

correctly   = 0.4

Step-by-step explanation:

Here given: The quiz has two questions.

Question 1 is an Multiple Choice Question with 5 options, out of which only one option is the correct option.

So, the probability of answering the question 1  correctly  = $(\frac{1}{5} ) = 0.2$

Question 2  is an true false question with 2 options, out of which only one option is the correct option.

So, the probability of answering the question 2  correctly  = $(\frac{1}{2} ) = 0.5$

Now, let us consider each part asked:

a. The probability that both questions are answered correctly

= (0.2)(0.5)  = 0.1

b. The probability that only one  questions is answered correctly

= 1 - [both right or both wrong] = 1 - [0.1 + (0.5)(0.8)] = 1-[0.5] = 0.5

c. The probability that none questions is answered correctly

= P(not Q1) x P(not Q2)  = (1- P(Q1) )(1- P(Q2))  = (1-0.5)(1-0.2)  = 0.4

d. The probability that only question 1 is answered correctly

= P( Q1) x P(not Q2)  = (1- P(Q1) )(P(Q2))  = (1-0.5)(0.2)  = 0.1

e. The probability that only question 2 is answered correctly

= P( not Q1) x P( Q2)  = (P(Q1) )(1-  P(Q2))  = (0.5)(1-0.2)  = 0.4