A binomial probability experiment is conducted with the given parameters.

A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment.
$n=5,p=0.85,x=3$
$P\left(3\right)=$
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Step 1
Given information:
A binomial probability experiment is conducted with the following given parameters:
$n=5$
$p=0.85$
$x=3$
Step 2
The above case can be represented as:
$X\sim B\in omial\left(n=5,p=0.85\right)$
The probability distribution function of X is:
$P\left(X=x\right){=}^{n}{C}_{x}{p}^{x}{\left(1-p\right)}^{n-x}$
The P(3) is calculated as follows:
$P\left(X=3\right){=}^{5}{C}_{3}{0.85}^{3}{\left(1-0.85\right)}^{5-3}$
${=}^{5}{C}_{3}×{0.85}^{3}×{0.15}^{2}$
$=0.1382$
Therefore, the required probability is 0.1382.