Question

A quiz consists of 10 multiple choice​ questions, each with five possible​ answers, one of which is correct. to pass the quiz a student must get​ 60% or better on the quiz. if a student randomly​ guesses, what is the probability that the student will pass the​ quiz

Answer 1

The probability is 0.006, or 0.6%.

This is binomial; there are a fixed number of trials (10), the events are independent (the chances of one occurring do not affect the chances of the other occurring), and there are two outcomes (either right or wrong).

He must get 6 of the 10 questions correct, so k is 6 and n is 10.  The probability of getting a question correct is 1/5=0.2; the probability of getting a question incorrect is 4/5=0.8.

$_{10}C_6\times(0.2)^6\times(1-0.2)^{10-6} \\ \\\frac{10!}{6!4!}\times(0.2)^6\times(0.8)^4 \\ \\210(0.2)^6\times(0.8)^4=0.0055\approx0.006$