Question

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%. If the probability of the employee being less than 30 years old given that the employee is a male is 40%, what is the probability that the employee is a male, given that the employee is less than 30 years old?
0.34
0.42
0.55
0.69
0.71

Answer 1

@kropot72

Answer 2

We want
$$
P(M|Y)
$$
Where Y is the event, employee is less than 30 years old.

How can we rewrite this in terms of the information given?

What is \(P(M)\)?
What is \(P(Y)\)?
What is \(P(Y|M)\)?

Rewriting the 1st probability in terms of the three immediately above will give you your answer.

Does this make sense?

Answer 3

heck no sorry

Answer 4

What does conditional probability mean to you?

Answer 5

event given that another event has occurred

Answer 6

So
$$
P(M|Y)=\cfrac{P(Y|M)P(M)}{P(Y)}
$$
Do you agree?
Have you seen this before?
Do you understand why?

Answer 7

At this point you could plug in your knowns and get your answer. But you need to know what each term represents to do that. You also need to know Baye's Theorem:

https://en.wikipedia.org/wiki/Bayes%27_theorem#Statement_of_theorem

$$
P(M|Y)=\cfrac{P(M\cap Y)}{P(Y)}\\
P(Y|M)=\cfrac{P(M\cap Y)}{P(M)}
$$
Put these two together, you have

$$
P(M|Y)=\cfrac{P(Y|M)P(M)}{P(Y)}
$$
If this doesn't look familiar. You may need to review the link above.

Answer 8

YES! BUT MY COMPUTER IS GOING TO DIE SO LL BE ON TOMROWO MAYBE AH THANKS THOUGH

Answer 9

Baye's Theorem - read about it

Answer 10

The above probability tree might help your understanding. We are given that the probability of the employee being less than 30 years old is 0.7. Therefore having calculated the probability of a randomly selected male being less then 30 years old as 0.24, if we subtract 0.24 from 0.7 we get the probability of a randomly selected female being less than 30 years old as 0.7 - 0.24 = 0.46.
The probability that the employee is a male, given that the employee is less than 30 years old is then found from:
\[\large P(male) = \frac{0.24}{0.70}=you\ can\ calculate\]