Probability of passing

Question

On average, the probability that James will correctly answer a question correctly on a science exam is 0.80. If an exam paper contains 10 questions and at least 9 correct answers is required to pass, find the probability that James will pass the science exam. 

Answer 1

P(Correct answer) = .8

P(incorrect) = .2

 

You can now solve this using the binomial distribution formula.

nCk * P(correct)^k * P(incorrect)^n-k

 

Where n is the total questions (10) and k is the number he needs to get correct.  So the probability of passing is P(9/10 correct) + P(10/10 correct).

 

P(9 correct) = 10C9 * .8^9 * .2^1 = .2684

 

P(10 correct) = 10C10 * .8^10 * .2^0 = .1073

 

.2684 + .1073 = .3757