Question

Approximately 10.3% of american high school students drop out of school before graduation. choose 10 students entering high school at random. find the probability that all 10 stay in school and graduate. round your answer to the nearest thousandth.

Answer 1

The probability that a binomial experiment of n trials and p, the probability of success, produces an outcome, x is given by:

$P(x)={ ^nC_r}p^x(1-p)^{n-x}$

Given that approximately 10.3% of american high school students drop out of school before graduation, thus p = 0.103.

If we choose 10 students (i.e. n = 10)

The probability that all 10 stay in school and graduate means the probability that none of the 10 students dropped out$P(0)={ ^{10}C_0}(0.103)^0(1-0.103)^{10} \\ \\ 1\times1\times(0.897)^{10}=0.337$ is given by