Question

According to government data, 70% 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

Answer:

Given,

p = 70% = 0.70

q = 1 - 0.70

= 0.30

sample n = 15

P(X = r) = nCr*p^r*q^(n-r)

a)

To determine the probability that exactly 2 of them have never been married

P(X = 2) = 15C2*0.70^2*0.30^13

= 0

b)

To give at most 2 of them have never been married

P(X <= 2) = P(x = 0) + P(x = 1) + P(x = 2)

= 15C0*0.70^0*0.30^15 + 15C1*0.70^1*0.30^14 + 15C2*0.70^2*0.30^13

= 0 + 0 + 0

= 0

c)

To give at least 13 of them have been married

Required probability = P(At most 2 never married)

= 0