1
$\begingroup$

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!

$\endgroup$
  • 1
    $\begingroup$ The events aren't independent. The second method you used is the correct one! $\endgroup$ – Pspl Aug 28 '19 at 15:57
1
$\begingroup$

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.

$\endgroup$
1
$\begingroup$

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.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.