Multiplication rule from frequency table, confusion I am studying the probability multiplication rule but there is something i don't get:
I have this frequency table:
frequency table
and say one sample is randomly picked up, if I want to calculate the probability of sampling one individual which is Male AND Infected my understanding is that as the two events are independent it should be:
Pmale=43/81
Pinfected=59/81
Pmale AND Infected=Pmale*Pinfected=0.386
but from the frequency table I see the actual number of infected man is 36, and 36/81 gives 0.4444...shouldn't these percentages be equal? what am i missing?
they turn out to be equal if the number of infected and not infected man and woman is the same (i.e  inf/not inf man=30 and inf/not inf woman=2).
sorry for the probably very basic question and thanks for your time! 
 A: The second method is correct.
The first method is wrong because when you select the man, the infection rate immediately changes. So the infection probability is $36/43$ and if you multiply this by the probability of selecting a man, you would get $0.44444$, the correct answer (your second method).
Think of it this way:
You have two bags of marbles. Bag A has Red and Green marbles and Bag B contains Blue and Yellow. If you want to calculate of picking a red marble, you calculate the probability of choosing from bag A instead of B and then multiply by the probability of getting Red from Bag A. Contents of bag B would not matter.
A: One way of checking if the events $A$ and $B$ are independent is calculate the conditional probability of one of them, let's say $P(A)$, and see if is the same as $P(A|B)$, or probability of $A$ occurs when $B$ already happened (actually you should check the in-dependency of two events by the very way you're using to calculate $P(A\cap B)$).
By this you easily conclude that, if $A$: the individual is male; $B$: the individual is infected:
$$P(A)=\frac{43}{81}\neq \frac{36}{59}=P(A|B)$$
So the events aren't independent.
