<h3>
a. The probability that both questions are answered </h3><h3>
correctly = 0.1 </h3><h3>
b. The probability that only one questions is </h3><h3>
answered correctly = 0.5</h3><h3>
c. The probability that none questions is </h3><h3>
answered correctly = 0.4</h3><h3>
d. The probability that only question 1 is </h3><h3>
answered correctly = 0.1</h3><h3>
e. The probability that only question 2 is answered</h3><h3>
correctly = 0.4</h3>
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 <u>one option is the correct option</u>.
So, the probability of answering the question 1 correctly = 
Question 2 is an true false question with 2 options, out of which only <u>one option is the correct option</u>.
So, the probability of answering the question 2 correctly = 
Now, let us consider each part asked:
a. The probability that <u>both questions are answered correctly </u>
= (0.2)(0.5) = 0.1
b. The probability that <u>only one questions is answered correctly </u>
= 1 - [both right or both wrong] = 1 - [0.1 + (0.5)(0.8)] = 1-[0.5] = 0.5
c. The probability that <u>none questions is answered correctly </u>
= 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<u> question 1 is answered correctly </u>
= P( Q1) x P(not Q2) = (1- P(Q1) )(P(Q2)) = (1-0.5)(0.2) = 0.1
e. The probability that only<u> question 2 is answered correctly </u>
= P( not Q1) x P( Q2) = (P(Q1) )(1- P(Q2)) = (0.5)(1-0.2) = 0.4