Question

A short quiz has two true-false questions and one multiple-choice question with four possible answers. A student guesses at each question. Assuming the choices are all equally likely and the questions are independent of each other, the following is the probability distribution of the number of answers guessed correctly. a. What is the Probability of two or more questions right?
b. What is the probability of at least one correct answer?

X 0 1 2 3

P(X) 0.1875 0.4375 0.3125 0.0625

Answer 1

Answer:

a) Probability of two or more questions right is 0.375.

b) Probability of at least one correct answer is 0.8125.

Step-by-step explanation:

Given : A short quiz has two true-false questions and one multiple-choice question with four possible answers. A student guesses at each question. Assuming the choices are all equally likely and the questions are independent of each other, the following is the probability distribution of the number of answers guessed correctly.

X           0                1             2                 3

P(X)   0.1875     0.4375     0.3125       0.0625

To find :

a) What is the Probability of two or more questions right?

b) What is the probability of at least one correct answer?

Solution :

a) Probability of two or more questions right is

$P_1=P(X=2)+P(X=3)$

$P_1=0.3125+0.0625$

$P_1=0.375$

Probability of two or more questions right is 0.375.

b) Probability of at least one correct answer is

$P_2=P(X\geq 1)$

$P_2=P(X=1)+P(X=2)+P(X=3)$

$P_2=0.4375+0.3125+0.0625$

$P_2=0.8125$

Probability of at least one correct answer is 0.8125.