# Probability of two events

1. Dec 7, 2013

### oneamp

Hello. I have two probability density functions for two events. I would like to find the probability that they both will occur at the same time. It is simply multiplying the results of the two integrals over the time, correct?

Thank you

2. Dec 7, 2013

### mathman

No. Two events can occur at the same time only if they have discrete distributions. When both have continuous distributions (and are independent) the probability of happening at the same time is 0.

3. Dec 7, 2013

### oneamp

Yes true :) How can I calculate the probability that between some points 'a' and 'b' in time, two events with these PDFs will occur? For example, if one PDF describes the probability that a light will be orange, and another PDF describes probability for a green light, and I want to know the chances that there will be an orange and a green light illuminated "at the same time" between times 'a' and 'b'?

Last edited: Dec 7, 2013
4. Dec 7, 2013

### Office_Shredder

Staff Emeritus
oneamp, if the two events are independent then you can simply multiply the probabilities of each even happening. If they have some dependence between each other then you need to know exactly what that dependence is - you have to have a pdf p(x,y) which is called the joint distribution between the two variables.

5. Dec 7, 2013

### oneamp

Thank you very much

6. Dec 9, 2013

### jbunniii

That's not true at all. Suppose $X$ and $Y$ are independent normally distributed random variables. Let $A$ be the event that $X > 0$ and $B$ be the event that $Y > 0$. Clearly the probability of $A \cap B$ is nonzero.

7. Dec 10, 2013

### mathman

You misunderstood the point of the original question. He was asking about something like the probability that X=Y when both have continuous distributions.