Statistics Homework Help!

Question

A surprise quiz contains three multiple-choice questions: Question 1 has four suggested answers. Question 2 has three, and Question 3 has two. A completely unprepared student decides to answer questions at random. Let X denote the number of questions the student answers correctly.

 

A)  list the possible values of x

 

B) find the probability distribution of X

 

C) Find P[At least 1 correct] = P[X greater than or equal to 1]. 

Answer 1

ABCD

ABC

AB

There are 24 ways to answer each question on the quiz: 4 × 3 × 2 = 24.

AAA BBB CCA DAA

AAB BBA CCB DAB

ABA BAB CBA DBA

ABB BAA CBB DBB

ACA BCA CAA DCA

ACB BCB CAB DCB

p = probability of answering Question #1 correctly = 0.25

q = probability of answering Question #2 correctly = 0.33

r = probability of answering Question #3 correctly = 0.50

P(X ≥ 1) = P(X = 1) + P(X = 2) + P(X = 3) or 1 - P(X = 0) [You can use the complement rule just to save time when it comes to taking the test]

We will use the formula:

C(n,k) = C(3,0) where n is the number of questions and k is the number of correct answers.

3! / (0!)*(3!) = 1 way to get none of the questions right.

Multiply by the 3 different probabilities to get 1*(0.75)*(0.67)*(0.50) = 0.25125

P(X ≥ 1) = 1 - 0.25125 = 0.74875

The probability of getting at least 1 question right is 0.74875 or approximately 0.75.