That seems like a really complicated way to look at an easy question that has been worded very difficultly.

I prefer tree-diagrams :p (apologies for the bad drawing)

http://i15.tinypic.com/6agehi0.jpg
Just follow the path that is relevant.

First, it asks about the husband - You are looking for the husband to be watching TV.. correct?

In this case, start at the left-hand side and follow the 'branch' up towards the a. 60% (watching)

Next, it asks about the wife.

When the Husband is watching TV, she must be watching at the same time.

So, next - continue up along that path to a. 40% (watching)

Now, all you need to do is multiply the %'s that you had on the way -

ie,

60% $\displaystyle \cdot$ 40% --- ie, find 40% of 60% [of 100]

or, if you prefer it like this:

$\displaystyle \frac {60}{100} \cdot \frac{60}{100} = \frac {6}{10} \cdot \frac{4}{10} = 0.6 \cdot 0.4 = 0.24$

Therefore, there is a 0.24 (24%) possibility of having the Husband AND Wife watching tv at the same time

Quote:

a.) Find the probability that if the wife is watching TV then the husband is also.

Assuming that should read WHEN the husband is also, this sounds about right