Question

According to government data, 26% of employed women have never been married. Rounding to 4 decimal places, if 15 employed women are randomly selected: a. What is the probability that exactly 2 of them have never been married? b. That at most 2 of them have never been married? c. That at least 13 of them have been married?

Answer 1

Solution :

Given that p = 0.26 , n = 15

=> q = 1 - p = 0.74

Formula :

=> For binomial distribution , nCr*p^r*q^(n-r)

=> nCr = n!/r!*(n-r)!  

a. P(x = 2) = 15C2*0.26^2*0.74^13

= 0.1416

b. P(x <= 2) = P(x = 2) + P(x = 1) + P(x = 0)

= 15C2*0.26^2*0.74^13 + 15C1*0.26^1*0.74^14 + 15C0*0.26^0*0.74^15

= 0.1416 + 0.0576 + 0.0109

= 0.2101

c. P(x >= 13) = P(x = 13) + P(x = 14) + P(x = 15)

= 15C13*0.26^13*0.74^2 + 15C14*0.26^14*0.74^1 + 15C15*0.26^15*0.74^0

= 0.00000149

= 0.0000 (rounded)