Hi

have i answered this question correctly

Given that P(X) = 0.5
P(Y) = 0.6
P(Y/X) = 0.9 find probabilites for

a. P(X and Y)

my answer: P(X) P(Y/X) = 0.5 * 0.9 = 0.45

B. P(X or Y)
my anwser

P (X or y) = P(X) + P(Y) - P(X and B) = 0.5 + 0.6 - 0.45 = 0.65

c. P(X/Y)

not sure about this one

thanks for your help
makbool

Hi makbool!!

The topic here is Conditional Probability, and the answer of the
problem c) is given in the solution of the problem a)!!:

You know that P(X and Y) = P(X) . P(Y/X) ; 
then 
P(Y/X) = P(X and Y) / P(X)
then
P(X/Y) = P(X and Y) / P(Y)
Why? 
Both events X and Y are Not Independent, so if you want to know the
probability that event X and event Y occur you must multiply the
probability that event X occur by the probability that event Y occur
GIVEN that event X has occured already. This is because for the event
(X and Y) it must be that the event X occur (and the probability of
this is P(X)), and then GIVEN X it must be that the event Y occur (and
the probability of this is P(Y/X)); then
P(X and Y) = P(X) . P(Y/X)
But here is the trick!!!
We can use first any of the events X or Y, in other words:
...for the event (X and Y) it must be that the event Y occur (and the
probability of this is P(Y)), and then GIVEN Y it must be that the
event X occur (and the probability of this is P(X/Y)); then
P(X and Y) = P(Y) . P(X/Y)

From the last formula we can obtain P(X/Y):

P(X/Y) = P(X and Y) / P(Y) 

For the problem c) we have:

P(X/Y) = 0.45 / 0.6 = 0.75

I hope this helps you. Please donīt hesitate to request for an answer
clarification if you need it.

Regards.
livioflores-ga

thanks for clarification
makbool