Question

Assume that when adults with smartphones are randomly selected, 58% use them in meetings or classes. If 6 adult smartphone users are randomly selected, find theprobability that exactly 3 of them use their smartphones in meetings or classes

Answer 1

Given that the sample contains 6 students, so the sample size will be,

`n=6`

Let the success of the experiment is defined as the event that a randomly selected adult uses a smartphone in meetings or classes. And 'x' be the random variable representing the number of successes.

Given that 58% of the adults use a smartphone in meetings and classes. So there will be 58% chance that a randomly selected adult uses a smartphone in meetings and classes.

So, the probability of success will be,

`\begin{gathered} p=58\text{ percent} \\ p=(58)/(100) \\ p=0.58 \end{gathered}`

Then, the probability of getting exactly 'x' successes, is given by,

`P(X=x)=^nC_x\cdot p^x\cdot(1-p)^(n-x)`

So, the probability of exactly 3 successes will be,

`\begin{gathered} P(X=3)=^6C_3\cdot(0.58)^3\cdot(1-0.58)^(6-3) \\ P(X=3)=20\cdot(0.195112)\cdot(0.074088) \\ P(X=3)\approx0.2891 \\ P(X=3)\approx28.91\text{ percent} \end{gathered}`

Thus, there is 28.91% probability that exactly 3 of them use their smartphones in meetings or classes.