Find the Probablility

Question

Assume that when adults with smartphones are randomly​ selected,

37% use them in meetings or classes. If 6 adult smartphone users are randomly​ selected, find the probability that exactly 3 of them use their smartphones in meetings or classes.

Answer 1

Greetings Brit,

This question is evaluating your ability to use and apply the binomial distribution formula appropriately.

Assume that when adults with smartphones are randomly​ selected, 37% use them in meetings or classes. If 6 adult smartphone users are randomly​ selected, find the probability that exactly 3 of them use their smartphones in meetings or classes.

There is a binary feel/decision to the problem situation, namely "adults who use their smartphones" and "adults that do not use their cellphones" in meetings or classes. This is the classic "black/white" decision outcome, so we apply binomial distribution model to solve this question.

The formula is as follows P(X) = _nC_x × p^x × q^{n -x}

p = probability of success → Yes, it will occur → .37

q = probability of failure → No, it will not occur → .63

n = total number of objects randomly selected → 6

x = number of objects selected from the total given → 3

Plug these into the formula and solve:

P(3) = ₆C₃ × (.37)³ × (.63)^{6 - 3} → ₆C₃ × (.37)³ × (.63)³ = 20×.050653×0.250047‬ = 0.25331261382

or 25.33% chance