Question

9 "good" and 1 "bad student" take the exam. good students successfully solve 35 out of 40 samples. Bad Student, on the other hand, can only solve 10 out of 40 examples successfully.
Random 1 student makes 1 error out of 6 questions.
What is the probability that the student will be a "bad student"?

Answer 1

The probability of the random student is dependent on three things

probability of being a bad student = 1 / 10 because there 1 bad out of total of 10.

probability of answering correctly = 10/40 = 0.25

Probability of answering incorrectly = 1 - P(correct) = 1 - 0.25 = 0.75

Random 1 student makes 1 error out of 6 questions.

That means there is one incorrect and 5 correct

P(bad student is the random) = P(bad student) * P(incorrect)¹ * P(correct)⁵

We multiply because answering questions are independent and happen as an intersecting probability

P(bad student is the random) = 1 / 10 * 0.75 * 0.25⁵  

Ans : 0.0000732