Question

Assume that when adults with smartphones are randomly​ selected, 44​% use them in meetings or classes. If 7 adult smartphone users are randomly​ selected, find the probability that at least 4 of them use their smartphones in meetings or classes.

Answer 1

This is a binomial problem where probability p = 0.44, sample size n = 7 and selection r = 4

we have to find the probability of at least 4 out of 7

we can write it as

P(at least 4) = 1- P(at most 3)

Where P(at most 3) = P(x=0) + P(x=1) + P(x=2) + P(x=3)

using the formula

where n = 7 and r = 0, we get

where n = 7 and r = 1, we get

where n = 7 and r = 2, we get

and

where n = 7 and r = 3, we get

Adding all calculated probabilities, we get

P(at most 3) = 0.01727+ 0.09499 + 0.2239+0.2932 = 0.6294

So, Probability of at least 4 = 1-P(at most 3) = 1-0.6294 = 0.3706

Therefore, required probability is 0.3706 (rounded to 4 decimals)