Question

In a large population of high school students, 20% have experienced math anxiety. if you take a random sample of 10 students from this population, the probability that exactly two students have experienced math anxiety is ____.

Answer 1

The probability is 0.302.

This is a binomial probability. There are two outcomes; the probabilities are independent; and there is a fixed number of trials. The probability is given by:


`_nC_r(p)^r(1-p)^(n-r) \\ \\=_(10)C_2(0.2)^2(1-0.2)^(10-2)=_(10)C_2(0.2)^2(0.8)^8 \\ \\=45(0.2)^2(0.8)^8=0.30199\approx0.302`