Question

assume that when adults with smartphones are randomly selected 15 use them in meetings or classes if 15 adult smartphones are randomly selected, find the probability that at least 4 of them use their smartphones

Answer 1

The probability that at least 4 of them use their smartphones is 0.1773.

Explanation:

We are given that when adults with smartphones are randomly selected 15% use them in meetings or classes.

Also, 15 adult smartphones are randomly selected.

Let X = Number of adults who use their smartphones

The above situation can be represented through the binomial distribution;

`P(X = r) = \binom{n}{r}* p^(r) * (1-p)^(n-r) ; n = 0,1,2,3,.......`

where, n = number of trials (samples) taken = 15 adult smartphones

r = number of success = at least 4

p = probability of success which in our question is the % of adults

who use them in meetings or classes, i.e. 15%.

So, X ~ Binom(n = 15, p = 0.15)

Now, the probability that at least 4 of them use their smartphones is given by = P(X
`\geq` 4)

P(X
`\geq` 4) = 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3)

=
`1- \binom{15}{0}* 0.15^(0) * (1-0.15)^(15-0)-\binom{15}{1}* 0.15^(1) * (1-0.15)^(15-1)-\binom{15}{2}* 0.15^(2) * (1-0.15)^(15-2)-\binom{15}{3}* 0.15^(3) * (1-0.15)^(15-3)`

=
`1- (1* 1* 0.85^(15))-(15* 0.15^(1) * 0.85^(14))-(105 * 0.15^(2) * 0.85^(13))-(455 * 0.15^(3) * 0.85^(12))`

= 0.1773