The probability of randomly selected employee shows the happening of that event. The probability that the employee is a male, given that the employee is less than 30 years old is 0.34.
What is Conditional probability?
Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.
The conditional probability is the happening of an event, when the probability of occurring of other event is given.
The probability of event A, given that the event B is occurred.
[tex]P(A|B)=\dfrac{P(A\cap B)}{P(B)}[/tex]
Given information-
The probability of a randomly selected employee of a company being male is 60%.
The probability of the employee being less than 30 years old is 70%.
The probability of the employee being less than 30 years old (employee is a male) is 40%.
The probability that the employee is a male, given that the employee is less than 30 years old has to be find out.
As, the probability of a randomly selected employee of a company being male is 60% and the probability of the employee being less than 30 years old (employee is a male) is 40%.
Thus the probability of employee is less than 30 years old given that the employee is male is,
[tex]P(<30|M)=0.4\times0.6\\P(<30|M)=0.24\\[/tex]
As the probability of the employee being less than 30 years old is 70%. Thus, the probability that the employee is a male, given that the employee is less than 30 years old is,
[tex]P(M|<30)=\dfrac{0.24}{0.7}\\P(M|<30)\cong0.34[/tex]
Hence the probability that the employee is a male, given that the employee is less than 30 years old is 0.34.
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