# Thread: Married, at uni, married and at uni etc.

1. ## Married, at uni, married and at uni etc.

Employment data of a company reveals that 72% of the workers are married, that 44% are uni grads and that half of the uni grads are married. What is the probability that a randomly chosen worked:

1) Is neither married nor a uni grad
2) Is married but not a uni grad
3) Is married or is a uni grad

2. Originally Posted by acevipa
Employment data of a company reveals that 72% of the workers are married, that 44% are uni grads and that half of the uni grads are married. What is the probability that a randomly chosen worked:

1) Is neither married nor a uni grad
2) Is married but not a uni grad
3) Is married or is a uni grad
Dear acevipa,

First define the events as,

A worker is married: A

A worker is a university graduate: B

It is given that, $P(A)=0.72,~ P(B)=0.44,~P\left(\frac{A}{B}\right)=0.50$

So you have to find,

1) $P(A'\cap{B'})$

2) $P(A\cap{B'})$

3) $P(A\cup{B})$

First you can use the definition of conditional probability, $P\left(\frac{A}{B}\right)=\frac{P(A\cap{B})}{P(B)}$ to find $P(A\cap{B})$.

Then using set identities you can solve this problem.

3. Originally Posted by acevipa
Employment data of a company reveals that 72% of the workers are married, that 44% are uni grads and that half of the uni grads are married. What is the probability that a randomly chosen worked:

1) Is neither married nor a uni grad
2) Is married but not a uni grad
3) Is married or is a uni grad
Start by drawing a Venn diagram. The numbers that go in each part are 0.50, 0.22, 0.22 and 0.06 (your job is to decide where these numbers go ....) The questions then become trivial, answer them directly from the Venn diagram.

4. Originally Posted by mr fantastic
Start by drawing a Venn diagram. The numbers that go in each part are 0.50, 0.22, 0.22 and 0.06 (your job is to decide where these numbers go ....) The questions then become trivial, answer them directly from the Venn diagram.

Thanks but how did you get 0.06?

5. Originally Posted by acevipa
Thanks but how did you get 0.06?
Draw the Venn diagram! All the numbers have to add up to 1 ....