Question

Assume that each of the n trials is independent and that p is the probability of success on a given trial. Use the binomial probability formula to find P(x). n=6, x=1, p=0.4P(x)=_____ (Round to 4 decimal places.)

Answer 1

Step 1

Given;

`\begin{gathered} n=6 \\ x=1 \\ p=0.4 \end{gathered}`

Step 2

State the binomial probability formula

`p(x)=n_(c_x)(p^x)(1-p)^(n-x)`
`\begin{gathered} n_(c_x)=(n!)/(x!(n-x)!) \\ n_(c_x)=(6!)/(1!(6-1)!) \end{gathered}`
`n_(c_x)=(720)/(120)=6`

Step 3

Find p(x) by substitution

`\begin{gathered} P(x)=6(0.4^1)(1-0.4)^(6-1) \\ P(x)=2.4(0.6)^5 \\ P(x)=0.186624 \\ P(x)\approx0.1866\text{ to 4 decial places} \end{gathered}`

Answer; P(x)=0.1866 approximately to 4 decimal places