The probability that a trainee will remain with a company is 0.6. The probability that an employee earns more than Rs. 30,000 per month is 0.5. The probability that an employee who is a trainee remained with the company or who earns more than Rs. 30,000 per month is 0.7. What is the probability that an employee earns more than Rs. 30,000 per month given that he is a trainee who stayed with the company?
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Given: Probability of trainee = 0.6
Probability of employee = 0.5
Probability of trainee earning above 30K = 0.7
To Find: Employee earning more than 30K is a trainee
Solution:
Probability that a trainee will remain with a company = 0.6. = P(R) = 0.6
Probability that an employee earns more than Rs.30, 000 per year = 0.5 =
P( 30 K) = 0.5
Probability that an employee is a trainee who remained with the company or who earns more than Rs.30, 000 per year = 0.7 = P(R or 30K) = 0.7
The probability that an employee earns more than Rs.30, 000 per will be -
P(30K | R) = P(30K and R)/P(R)
= P(10K and R) = P(R)+P(30K)-P(30K or R)
= 0.6+0.5-0.7
= 0.4
Therefore P(30K |R)
= 0.4/0.6
= 2/3
Answer: The probability is 2/3.
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