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#job-applications
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#probability
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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?
Anonymous
Mar 3
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?
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ChatGPT
Mar 3
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.
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.
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