# Thread: Probability problem

1. ## Probability problem

The question:

Employment data at a large company reveals that 72% of the workers are married, that 44% are university graduates and that half of the university graduates are married. What is the probability that a randomly chosen worker...

a) is neither married nor a university graduate?
b) is married but not a university graduate?
c) is married or is a university graduate?

My attempt:
I tried to convert the wording into math as follows,

Let M = "people married"
Let G = "people graduated"

$P(M) = 0.72$
$P(G) = 0.44$
$P(M \cap G) = P(G)/2 = 0.22$

a) We want to find $P(M^c \cap G^c)$, so:

$P(M^c) = 1 - P(M) = 0.28$
$P(G^c) = 1 - P(G) = 0.56$

Thus we get 0.28 x 0.56 = 0.1568

However, this is incorrect. I'm sure I've made a wrong assumption somewhere. I'm yet to attempt part b) and c) since I'm not sure where I've gone wrong with a). Any assistance would be great.

2. Originally Posted by Glitch
The question:

Employment data at a large company reveals that 72% of the workers are married, that 44% are university graduates and that half of the university graduates are married. What is the probability that a randomly chosen worker...

a) is neither married nor a university graduate?
b) is married but not a university graduate?
c) is married or is a university graduate?

My attempt:
I tried to convert the wording into math as follows,

Let M = "people married"
Let G = "people graduated"

$P(M) = 0.72$
$P(G) = 0.44$
$P(M \cap G) = P(G)/2 = 0.22$

a) We want to find $P(M^c \cap G^c)$, so:

$P(M^c) = 1 - P(M) = 0.28$
$P(G^c) = 1 - P(G) = 0.56$

Thus we get 0.28 x 0.56 = 0.1568

However, this is incorrect. I'm sure I've made a wrong assumption somewhere. I'm yet to attempt part b) and c) since I'm not sure where I've gone wrong with a). Any assistance would be great.
Have you drawn a Venn Diagram?

3. No I haven't. Probably a good idea. Will report back.

4. Hello, Glitch!

Employment data at a large company reveals that 72% of the workers are married,
44% are university graduates, and half of the university graduates are married.

What is the probability that a randomly chosen worker:

a) is neither married nor a university graduate?
b) is married but not a university graduate?
c) is married or is a university graduate?

Did you consider entering all this data into a chart?

. . $\begin{array}{c||c|c||c|}
& \text{Grad} & \text{non-G} & \text{Total} \\ \hline \hline
\text{Married} & 22\% & 50\% & 72\% \\ \hline
\text{Single} & 22\% & 6\% & 28\% \\ \hline \hline
\text{Total} & 44\% & 56\% & 100\% \\ \hline \end{array}$

5. Thanks guys. I used a Venn diagram and worked it out. Cheers.