Out of 60 applicants for a job position, 40 are from rongo. If 20 applicants are selected at random, what is the probability that 10 will be fro rongo?

To find the probability that 10 out of the 20 selected applicants will be from Rongo, we can use the binomial probability formula:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

where:
- n = total number of applicants selected (20)
- k = number of applicants from Rongo selected (10)
- p = probability of selecting an applicant from Rongo (40/60 = 2/3)

Plugging in the values:

P(X = 10) = (20 choose 10) * (2/3)^10 * (1 - 2/3)^(20-10)
P(X = 10) = (184,756) * (2/3)^10 * (1/3)^10
P(X = 10) = 184,756 * (0.002251) * (0.01745)
P(X = 10) ≈ 0.064

Therefore, the probability that exactly 10 out of the 20 selected applicants will be from Rongo is approximately 0.064.