My Problem:
The random variables X and Y have the simultaneous probability function pX,Y(x, y).
| pX,Y(x, y) | X = 0 | X = 1 | X = 2 |
|---|---|---|---|
| Y = 0 | 0.1 | 0.2 | 0.1 |
| Y = 1 | 0.2 | 0.3 | 0.1 |
What is P(X > 0 | Y = 1) ?
Answer:
The answer to this problem should be 2/3
My attempt of solving it:
P(X = 1| Y = 1) = 0.3
P(X = 2| Y = 1) = 0.1
P(X > 0| Y = 1) = P(X = 1| Y = 1) + P(X = 2| Y = 1) = 0.4
My Question:
I am clearly getting the wrong answer, I would be very thankful for any help.
Your approach is not correct, you need to use conditional probability. If you have not seen the following formula before, you should try and find "conditional probability" or "Bayes theorem" on youtube/in a textbook. $P(X>0| Y=1)= \frac{P(X>0 \cap Y=1)}{P(Y=1)}=\frac{0.3+0.1}{0.2+0.3+0.1}=\frac{2}{3}$