Question

Rework problem 17 from section 4.1 of your text about a multiple-choice test in which each question has 4 choices only one of which is correct. Assume that 9 questions are answered by guessing randomly. What is the probability of getting exactly 4 correct answers?

Answer 1

Answer:

probability that exactly 4 out of 9 questions are correct   is 0.111

Step-by-step explanation:

Given data:

Test consist of multiple choice question which as 4 choices

Total number of answer randomly = 9

Probability of having 4 answer correctly is calculated as

p = probability of having particular question is answered in correct way  

  = 1/4 = 0.25

q = probability of having particular question is answered incorrectly  

  = 3/4 = 0.75

Binomial expansion is beneficial in various situations at which   numerical  variables are present that are countable or whole numbers 

probability that exactly 4 out of 9 questions are correct  

 $= ^9C_4 (0.25)^4 (0.75)^5$

  $= 120\ times 0.00390 \times 0.2373$

   = 0.111