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?
Solution :
n = 9
p = 0.3333
Using binomial probability formula ,
P(X = x) = (n C x) * px * (1 - p)n - x
P(X 7) = P(x = 7) + P(x = 8) + P(x = 9)
= (9 C 7) * 0.33337 * (0.6667)2 + (9 C 8) * 0.33338 * (0.6667)1 + (9 C 9) * 0.33339 * (0.6667)0
Probability = 0.0083
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