What is the probability of the same event happening to two (or more) different independent people within a specified time frame?
For example, if I wave my hands to my friend, there is a probability of 1/2 that he will wave back after a second. Or, he will wave back after 2 seconds with the same probability. What is the probability of two of my friends waving back at the same time at a specific instant (assuming the same probability and timing of 1-2 seconds)? How about three or more?
time p1 p2 probability 1s wave wave 1/2 -> probability of both p1 and p2 to wave back here! 2s wave wave 1/2 -> or here
I know the more people there are, the higher the probability for more of my friends to wave back to me at the same time. But how do I prove this mathematically?