Question

Let X be the number of successes in six independent trials of a binomial experiment in which the probability of success is
p = 2/5


Find the following probabilities. (Round your answers to four decimal places.)
(a) P(X = 5)



(b) P(3 ≤ X ≤ 5)

Answer 1

This is plug and chug.

Answer 2

\[
\mathcal P(X=k) = {n\choose k}p^k(1-p)^{n-k}={6\choose k}\left(\frac 25\right)^k\left(\frac 35\right)^{6-k}
\]

Answer 3

\[
\mathcal P(a\leq X\leq b) = \sum_{k=a}^{b}P(X=k) = \sum_{k=a}^{b}{6\choose k}\left(\frac 25\right)^k\left(\frac 35\right)^{6-k}
\]