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The probability that a trainee will remain with a company is 0.8 . The probability that an employee earns more than Rs.20,000 per month is 0.4 .The probability that an employee ,who was the trainee and remained with company or who earns more than 20,000 per month is 0.9 .What is the probability that an employee earns more than 20,000 per month given that he is a trainee, who stayed with the company?
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The probability that a trainee will remain with a company is 0.8 . The...
Solution:

Given probabilities are:
P(trainee stays with company) = 0.8
P(employee earns more than Rs.20,000 per month) = 0.4
P(trainee stays with company or earns more than Rs.20,000 per month) = 0.9

We need to find the probability that an employee earns more than Rs.20,000 per month given that he is a trainee, who stayed with the company.
Let's solve this using Bayes' Theorem.

Bayes' Theorem:
P(A|B) = P(B|A) * P(A) / P(B)
where,
P(A|B) is the probability of A given B has occurred
P(B|A) is the probability of B given A has occurred
P(A) is the marginal probability of A
P(B) is the marginal probability of B

Let's assume,
A = employee earns more than Rs.20,000 per month
B = trainee stays with company

We need to find P(A|B)

Step 1: Find P(B)
P(B) = P(trainee stays with company) = 0.8

Step 2: Find P(A)
P(A) = P(employee earns more than Rs.20,000 per month) = 0.4

Step 3: Find P(B|A)
P(B|A) = P(trainee stays with company or earns more than Rs.20,000 per month) / P(A)
P(B|A) = 0.9 / 0.4 = 2.25

Step 4: Find P(A|B)
P(A|B) = P(B|A) * P(A) / P(B)
P(A|B) = 2.25 * 0.4 / 0.8
P(A|B) = 1.125

Therefore, the probability that an employee earns more than Rs.20,000 per month given that he is a trainee, who stayed with the company is 1.125 or 112.5%. However, this answer is not possible as probability cannot be greater than 1. It seems like there is an error in given probabilities.
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The probability that a trainee will remain with a company is 0.8 . The probability that an employee earns more than Rs.20,000 per month is 0.4 .The probability that an employee ,who was the trainee and remained with company or who earns more than 20,000 per month is 0.9 .What is the probability that an employee earns more than 20,000 per month given that he is a trainee, who stayed with the company?
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