Don't Know how to work out this question:
An advertising executive studied TV viewing habits of married men and women during prime time hours. He determined that during prime time, husbands watch TV 60% of the time. When the husband is watching TV, 40% of the time the wife is also watching. When the husband is not watching, 30% of the time the wife is.
a.) Find the probability that if the wife is watching TV then the husband is also.
That seems like a really complicated way to look at an easy question that has been worded very difficultly.
I prefer tree-diagrams (apologies for the bad drawing)
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 -
60% 40% --- ie, find 40% of 60% [of 100]
or, if you prefer it like this:
Therefore, there is a 0.24 (24%) possibility of having the Husband AND Wife watching tv at the same time
Assuming that should read WHEN the husband is also, this sounds about righta.) Find the probability that if the wife is watching TV then the husband is also.
the question was: given that the wife is watching what is the probability that the husband is also watching
that just seems like a 'fancy' way of asking what is the probability of them both watching at the same time? ie, the wife is watching tv, what is the probability of the husband being there also?
Find the probability that if the wife is watching TV then the husband is also
After some thought, this could mean "what is the probability of the wife watching on her own, and then the husband coming to join her?" or "what is the probability of the wife watching tv on her own, and then she leaves, and then the husband comes in to watch on his own?"
which would be 12% 24% = 0.12 0.24 = 0.0288 = 2.88%
(btw, you forgot a bracket )
see my note in the quote up there .. im probably mistaken, but doesnt (w|h) mean w OR h ? ie, not w AND h ?Bayes Theoerm:
P(h|w).P(w)=P(h and w)
P(w) = P(w|h)P(h) + P(w| not(h))P(not(h)) = 0.4*0.6 + 0.3*0.4 = 0.36
are you calculating the husband AND wife together + the wife on her own??
P(h and w) = 0.4*0.6 = 0.24
P(h|w) = P(h and w)/P(w) = 0.24/0.36 = 2/3 ~= 0.6667
looking at the last line on there, it seems like you are answering "(1) what is the probability of the husband and wife watching together?" and "(2) the probability of the wife leaving - leaving the husband to watch on his own"
then resulted in dividing (1)/(2)
I was always taught to multiply probabilities (in the majority of circumstances, if not, all) becuase this combines them.
you have said that the chance of the husband and wife watching together, is smaller than than the chance of them watching together and then the wife leaving? this just doesnt make sense.