Question

According to the Statistics Canada website, the unemployment rate in Canada is approximately 7.4 % of the eligible workforce. If 25 members of the eligible workforce are randomly selected, and it is determined that at least 2 of the 25 are unemployed, what is the probability that exactly 4 of the 25 members are unemployed?

Answer 1

If X = Number of those unemployed within the sample size,

Then,
X should be Binomial (25,0.074)

Therefore, for X = 4;

P(X=4|X≥2) = [P(X=4) and P(X≥2)]/P(X≥2) = P(X=4)/P(X≥2) = P(X=4)/[1-P(X=0)-P(X=1)]

Now;
P(X=4) = (25C4)*0.074^4*(1-0.074)^(25-4) = 0.0755
P(X=0) = (25C0)*0.074^0*(1-0.074)^(25-0) = 0.1463
P(X=1) = (25C1)*0.074^1*(1-0.074)^(25-1) = 0.2923

Substituting;
P(X=4|X≥2) = 0.0755/(1-0.1463-0.2923) = 0.1345