The probability of getting fewer than 3 correct answers is 0.1385
<h3>How calculate the probability of getting fewer than 3 correct answers?</h3>
This is a binomial problem with n = 13
Since we are dealing with a binomial probability distribution. We are going to use the binomial distribution formula for determining the probability of x successes:
P(x = r) = nCr . p^r . q^n-r
total choices = 13 x 3 = 39
p = P(correct answer) = 13/39 =1/3
Given: n = 13, p = 1/3, q = 1- 1/3 = 2/3
Fewer than 3 correct answers mean less than 3 correct answers
P(x<3) = P(x = 0) + P(x=1) + P(x=2)
P(x<3) = (13C0 × (1/3)^0 × (2/3)^13-0) + (13C1 × (1/3)^1 × (2/3)^13-1 + (13C2 × (1/3)^2 × (2/3)^13-2)
= 0.005138 + 0.0333 + 0.1001
= 0.1385
Therefore, the probability that the person gets fewer than 3 correct answers is 0.1385
Learn more about binomial distribution on:
brainly.com/question/29220138
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