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"

$\displaystyle P(M) = 0.72$

$\displaystyle P(G) = 0.44$

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

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

$\displaystyle P(M^c) = 1 - P(M) = 0.28$

$\displaystyle P(G^c) = 1 - P(G) = 0.56$

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.