Question

A binomial probability experiment is conducted with the given parameters. Compute the probability of successes in the n independent trials of the experimentn = 9, p=0.2, x<_3The probability of x<_3 successes is(Round to four decimal places as needed.)

Answer 1

$\begin{gathered} \text{Equation } \\ P(x)\text{ = }\frac{n!}{(n\text{ - x)!x!}}p^xq^{n\text{ - x}} \\ \text{Substitution} \end{gathered}$$\begin{gathered} P(3)\text{ = }\frac{9!}{(9\text{ - 3)!3!}}(0.2)^3(0.8)^{9\text{ - 3}} \\ P(3)\text{ = }\frac{362880}{(720)(6)}(0.008)(0.262) \\ P(3)\text{ = }\frac{362880}{4320}(0.002096) \\ P(3)\text{ = 84(0.002096)} \\ P(3)\text{ = 0.1}761 \end{gathered}$

Result: P(3) = 0.1761