# Probability of two events

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

mathman
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

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.

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'?

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Office_Shredder
Staff Emeritus
Gold Member
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.

1 person
Thank you very much

jbunniii