91Ó°ÊÓ

A group of 20 adult smartphone users is selected. The probability of selecting a user who uses his/her smartphone in meetings or classes is equal to 0.54.

Let X denote the users who use their smartphones in meetings or classes.

Let success be defined as selecting a user who uses his/her smartphone in meetings or classes.

The number of trials (n) is given to be equal to 20.

The probability of success is calculated below:

$$\begin{gathered} p=54\% \\ =\frac{54}{100} \\ =0.54 \end{gathered}$$

The probability of failure is calculated below:

$$\begin{gathered} q=1-p \\ =1-0.54 \\ =0.46 \end{gathered}$$

The number of successes required in 20 trials should be equal to x=15.

The binomial probability formula is as follows:

$P\left(X=x\right)={}^n{C}_x{\left(p\right)}^x{\left(q\right)}^{n-x}$

By using the binomial probability formula, the probability of getting 15 users who use their smartphones in meetings or classes is computed below:

$$\begin{gathered} P\left(X=15\right)={}^{20}{C}_{15}{\left(0.54\right)}^{15}{\left(0.46\right)}^{20-15} \\ =\frac{20!}{15!\left(20-15\right)!}{\left(0.54\right)}^{15}{\left(0.46\right)}^5 \\ =0.0309 \\ ≈0.031 \end{gathered}$$

Therefore, the probability of getting 15 users who use their smartphones in meetings or classes is equal to 0.031.