a test consists of 10 multiple choice . to pass the test a student must answer exactly 5 of the questions correctly. if a student guesses on each question, what is the probability that the student will pass the test

Complete question :

A test consists of 10 multiple choice questions. Each question has 5 choices. To pass the test, a student must answer at least 6 questions correctly. If a student guesses on each question, the probability of getting it right is 20%. What is the probability that the student will pass the test?

0.006370

Step-by-step explanation:

Number of options = 5, with only one correct,hence, p = 1/5 = 0.2

Number of questions = 10

Number of correct answers required to pass = 6

Using binomial distribution formula :

P(x =x) = nCx * p^x * (1 - p)^(n - x)

p = 0.2 ; 1 - 0.2 = 0.8

n = 10 ; x = 6

P(x ≥ 6) = p(6) + p(7) + p(8) + p(9) + p(10)

The formula above can be used to obtain the individual probabilities then taking the sum or we can obtain the solution using a calculator ;

Using a binomial probability distribution calculator with the parameters given :

P(x ≥ 6) = 0.0063693824

= 0.006370 ( 4 decimal places)