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?
Answer:
0.006370
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)