In Exercises 21–24, assume that when adults with smartphones are randomly selected, 54% use them in meetings or classes (based on data from an LG Smartphone survey).

If 10 adult smartphone users are randomly selected, find the probability that at least 8 of them use their smartphones in meetings or classes.

A group of 10 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 10 trials should be at least eight.

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 at least eight users who use their smartphones in meetings or classes is computed below:

$$\begin{gathered} P\left(X⩾8\right)=P\left(X=8\right)+P\left(X=9\right)+P\left(X=10\right) \\ ={}^{10}{C}_8{\left(0.54\right)}^8{\left(0.46\right)}^{10-8}+{}^{10}{C}_9{\left(0.54\right)}^9{\left(0.46\right)}^{10-9}+{}^{10}{C}_{10}{\left(0.54\right)}^{10}{\left(0.46\right)}^{10-10} \\ =0.068845+0.017960+0.002108 \\ =0.088913 \\ =0.0889 \end{gathered}$$

Therefore, the probability of getting at least eight users who use their smartphones in meetings or classes is equal to 0.0889.