Question

According to government data, 43% of employed women have never been married. Rounding to 4 decimal places, if 15 employed women are randomly selected: 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

Let X be the number of employed women have never been married in 15 randomly selected employed women.

Then X ~ Binomial(n = 15, p = 0.43)

a.

P(X = 2) = ¹⁵C₂ * 0.43² * (1 - 0.43)^15-2 = 15! / ((15-2)! * 2!) * 0.43² * 0.57¹³

= 105 * 0.43² * 0.57¹³

= 0.0130

b.

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

= ¹⁵C₀ * 0.43⁰ * (1 - 0.43)^15-0 + ¹⁵C₁ * 0.43¹ * (1 - 0.43)^15-1 + ¹⁵C₂ * 0.43² * (1 - 0.43)^15-2

= 0.0002 +  0.0025 +  0.0130

= 0.0157

c,

P(X 13) = P(X = 13) + P(X = 14) + P(X = 15)

= ¹⁵C₁₃ * 0.43¹³ * (1 - 0.43)^15-13 + ¹⁵C₁₄ * 0.43¹⁴ * (1 - 0.43)^15-14 + ¹⁵C₁₅ * 0.43¹⁵ * (1 - 0.43)^15-15

= 0.000586 +  0.000063 +  0.000003

= 0.0007