Question

n=10 p=0.7 x=8 P(8)=A binomial probability experiment is conducted with the given parameters. Compute the probability of X successes in the end independent trials of the experiment

Answer 1

The formula to compute the binomial probability is given to be:

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

where

$\begin{gathered} n=\text{ number of trials} \\ p=\text{ probability} \\ x=\text{ number of successes} \end{gathered}$

The binomial coefficient is defined by:

${{{{{n\choose x}}}}}=\frac{n!}{x!(n-x)!}$

The parameters provided in the question are:

$\begin{gathered} n=10 \\ p=0.7 \\ x=8 \end{gathered}$

Therefore, we can begin solving by calculating the binomial coefficient:

${{{n\choose x}}}=\frac{10!}{8!(10-8)!}=\frac{10!}{8!\cdot2!}=45$

Hence, we can calculate the probability to be:

$\begin{gathered} P(8)=45\times0.7^8\times(1-0.7)^{10-8} \\ P(8)=45\times0.7^8\times0.3^2 \\ P(8)=0.2334744405 \end{gathered}$

ANSWER:

In 3 decimal places, the probability is 0.233.