This question aims to find the **probability of adults** using smartphones in meetings or classes when phone users are **randomly selected. **

One of the largest smartphone manufacturersÂ **LG** surveyed smartphone usage among adults in the social environment like **meetings and classes** and it was found that **54% of the adults** use smartphones in meetings and classes.

Assuming a certain number of smartphone users are selected randomly, we can find the probability of these users using smartphones. If we select **8** adult smartphone users randomly in meetings or classes, we can easily find the probability of **6** **smartphone users.Â **

**Probability** is defined as the **number of chances** in which an event can occur randomly. It gives the **possible outcomes** of the **occurrence** of an event.

There is various kind of probabilities. Some of them are theoretical probability, experimental probability, and axiomatic probability.

## Expert Answer

The given data is as follows:

\[ p = 54 % \]

\[ p = \frac { 54 } { 100 } = 0 . 54 \]

\[ n = 8 \]

Where **p is the percentage** of smartphone users and **n** is the **total number** of randomly selected users.

**Binomial probability** is the type of probability that takes **two outcomes** of an event. One of the two outcomes is **success** which is more likely expected while the other outcome is a **failure**.

The formula of binomial probability is:

\[Â Â PÂ (Â XÂ =Â xÂ )Â =Â \frac {Â nÂ !Â }Â {Â xÂ !Â (Â nÂ –Â xÂ )Â ! } . pÂ ^Â x. (Â 1Â –Â p )Â ^Â {Â nÂ –Â x }Â \]

By putting values in the formula:

\[Â PÂ (Â XÂ =Â 6 ) =Â \fracÂ { 8 ! } {Â 6 ! (Â 8Â –Â 6Â )Â !Â } . 0 . 54Â ^Â 6 . (Â 1Â –Â 0 . 54Â ) ^Â {Â 8Â –Â 6Â }Â Â \]

\[Â PÂ (Â XÂ =Â 6 ) =Â \fracÂ { 8 ! } {Â 6 ! (Â 2Â )Â !Â } . 0 . 54Â ^Â 6 . (Â 1Â –Â 0 . 54Â ) ^Â {Â 2 }Â Â \]

\[Â PÂ (Â XÂ =Â 6 ) =Â 28 . 0 . 54Â ^Â 6 . 0Â .Â 46Â ^Â 2Â Â \]

\[Â PÂ (Â XÂ =Â 6 )Â \approx 0 . 1469Â \]

## Numerical Solution

**The probability of adults using smartphones in meetings or classes is approximately $ 0.1469 % $.**

## Example

Samsung surveyed the users of smartphones and found that **44% of adults** use smartphones in social gatherings. Find the probability of **6 adult** users out of **8** randomly selected users.

\[Â Â PÂ Â (Â XÂ Â =Â Â 6 )Â =Â Â \frac {Â 8 !Â }Â {Â 6 !Â (Â 8Â –Â 6 )Â !Â } . 0 . 44Â ^Â 6 . (Â 1Â –Â 0 . 44 )Â ^Â {Â 8Â –Â 6Â }Â Â \]

\[Â PÂ (Â XÂ =Â 6 ) = 28 . 0 . 44Â ^Â 6 . 0Â .Â 56Â ^Â 2Â \]

\[Â PÂ (Â XÂ =Â 6 ) \approxÂ 0 . 0637 \]

The probability of Samsung users out of 8 users is $ 0. 637 % $

*Image/Mathematical drawings are created in Geogebra**.*