Question

Assume that when adults with smartphones are randomly selected, 35% use them in meeting or classes. if 7 adults smartphones users are randomly selected, find the probability that exactly 4 of them use their smartphones in meeting or classes.
The probability is

Answer 1

This is a binomial probability problem
p = 0.35 = chance of picking 1 person who uses smartphones during meeting/class

n = 7 = sample size

k = 4 = target number of people who use their smartphone

Compute nCk = 7C4 using the nCr combination formula

nCr = (n!)/(r!*(n-r)!)
7C4 = (7!)/(4!*(7-4)!)
7C4 = (7*6*5*4!)/(4!*3!)
7C4 = (7*6*5)/(3!)
7C4 = (210)/(6)
7C4 = 35

Use this coefficient to find the binomial probability
B(k) = binomial probability for input k
B(k) = (nCk)*(p^k)*(1-p)^(n-k)
B(4) = (7C4)*(0.35^4)*(1-0.35)^(7-4)
B(4) = 35*(0.35^4)*(0.65)^3
B(4) = 0.144238

So the approximate answer is 0.144238
This value is accurate to 6 decimal places