Question

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. 10,000 per month is 0.7. What is the probability that an employee earns more than Rs. 10,000 per month given that he is a trainee who stayed with the company?

Answer 1

The probability that an employee earns more than Rs. 10,000 per month given that he is a trainee who stayed with the company is 0.667.

Step-by-step explanation:

We are given that the probability that a trainee will remain with a company is 0.6. The probability that an employee earns more than Rs. 10,000 per month is 0.5.

The probability that an employee who is a trainee remained with the company or who earns more than Rs. 10,000 per month is 0.7.

Let the Probability that a trainee will remain with a company = P(R) = 0.6

Probability that an employee earns more than Rs. 10,000 per month = P(More than 10,000) = 0.5

Probability that an employee who is a trainee remained with the company or who earns more than Rs. 10,000 per month = $P(R \bigcup \text{More than 10,000})$ = 0.7

As we know that;

$P(R \bigcup \text{More than 10,000})=P(R)+P(\text{More than 10,000}) - P(R \bigcap \text{More than 10,000})$Here, $P(R \bigcap \text{More than 10,000})$ = Probability that an employee who is a trainee remained with the company and who earns more than Rs. 10,000 per month

So,              $0.7=0.6+0.5 - P(R \bigcap \text{More than 10,000})$

             $P(R \bigcap \text{More than 10,000}) = 1.1-0.7$

             $P(R \bigcap \text{More than 10,000}) = 0.4$

Now, probability that an employee earns more than Rs. 10,000 per month given that he is a trainee who stayed with the company is given by = P(More than Rs. 10,000 / R)

The conditional probability of P(More than Rs. 10,000 / R) is given by;

         P(More than Rs. 10,000 / R) = $\frac{P(R \bigcap \text{More than 10,000}) }{P(R)}$

                                                        =  $\frac{0.4}{0.6}$ = 0.667

Therefore, the required conditional probability is 0.667.