Question

A student guesses on every question of a​ multiple-choice test that has 9 ​questions, each with 3 possible answers. what is the probability that the student will get at least 7 of the questions​ right

Answer 1

This is a binomial related problem. In this case,

P(correct) = p = 1/3
P(wrong) = q = 1-p = 1-1/3 = 2/3

The general formula for binomial is;
Summation [nCk(p)^k(q)^(n-k)]

Where
n = 9
k = 7,8,9

Substituting;
P(7≤X≤9) = [9C7(1/3)^7(2/3)^2]+[9C8(1/3)^8(2/3)^1]+[9C9(1/3)^9(2/3)^0] = [16/2187]+[2/2187]+[1/19683]=163/19683 ≈ 0.00828

Therefore, the  probability of getting atleast 7 question right is 0.00828.