Question

Assume that when adults with smartphones are randomly​ selected, 5454​% use them in meetings or classes. If 1515 adult smartphone users are randomly​ selected, find the probability that exactly 1010 of them use their smartphones in meetings or classes. The probability is

Answer 1

The probability is 0.1304 = 13.04%.

Explanation:

For each adult, there are only two possible outcomes. Either they use their smartphone in meetings or classes, or they do not. The probability of an adult using their smartphone in meetings or classes is independent of other adults. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

In which
`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

And p is the probability of X happening.

54​% use them in meetings or classes.

This means that
`p = 0.54`

If 15 adult smartphone users are randomly​ selected, find the probability that exactly 10 of them use their smartphones in meetings or classes.

This is P(X = 10) when n = 15. So

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

`P(X = 10) = C_(15,10).(0.54)^(10).(0.46)^(5) = 0.1304`

The probability is 0.1304 = 13.04%.