Question

Van guessed on all 8 questions of a multiple-choice quiz. Each question has 4 answer choices. What is the probability that he got exactly 1 question correct? Round the answer to the nearest thousandth.
0.033
0.267
0.733
0.801

Answer 1

Answer:

0.267

Step-by-step explanation:

This can be solved using the binomial probability formula which is:

$P(success)=nCk*p^{k}(1-p)^{n-k}$

Where

n is total number of trials (here, the total number of questions is 8, so n = 8)

k is the number of attempts we are looking for (here, we want to find probability of 1 question correct, so k = 1)

p is the probability of success (here, success is getting a questions right. Since there are 4 choices and 1 is right, probability of right = 1/4)

Plugging all the info into the formula we get:

$P(success)=nCk*p^{k}(1-p)^{n-k}\\P(1QuestionRight)=8C1*(\frac{1}{4})^{1}(1-\frac{1}{4})^{8-1}\\P(1QuestionRight)=\frac{8!}{(8-1)!*1!}(\frac{1}{4})(\frac{3}{4})^7\\P(1QuestionRight)=\frac{8!}{7!*1!}(\frac{1}{4})(\frac{3}{4})^7\\P(1QuestionRight)=8(\frac{1}{4})(\frac{3}{4})^7\\=0.267$

Second choice is right.