Question

A pop quiz has two questions. Question 1 is a multiple choice question with 4 possible answers. Question 2 is a true/false question. One student is completely unprepared for the quiz and has to guess the answers. Let X denote the number of questions answered correctly.

1. List all possible results for the student's quiz and their probabilities. Use C to denote a correct answer and I to denote and incorrect answer.

2. List the possible values for X.

3. Find the probabilities for each value of X and form the probability distribution.

4. Find the probability that the student gets at least 1 question correct.

5. Find the mean and standard deviation of this distribution using a graphing utility.

6. Find the expected number of questions the student will answer correctly.

Answer 1

(there are more than 4 parts, as per policy i am answering first 4 parts)

1.

P(C question 1) = 1/no. of choices = 1/4

P(I question 1) = 1 - 1/no. of choices = 1 - 1/4 = 3/4

P(C question 2) = 1/no. of choices = 1/2

P(I question 2) = 1 - 1/no. of choices = 1 - 1/2 = 1/2

(ques 1 , ques 2)	Probability
(C,C)	1/4 * 1/2 = 1/8
(C,I)	1/4 * 1/2 = 1/8
(I,C)	3/4 * 1/2 = 3/8
(I,I)	3/4 * 1/2 = 3/8

2.

out of two question you can get all wrong, 1 correct or both correct

therefore,

X = {0,1,2}

3.

P(X=0) = P(I,I) = 3/4 * 1/2 = 3/8

P(X=1) = P(C,I) + P(I,C) = 1/4 * 1/2 + 3/4 * 1/2 = 4/8 = 1/2

P(X=2) = P(C,C) = 1/4 * 1/2 = 1/8

4.

atleast 1 correct X>=1

P(X>=1) = P(X=1) + P(X=2)

= 1/2 + 1/8

= 5/8 = 0.625

P(atleast 1 correct) = 0.625

(please UPVOTE)