Question

Event A has a 90% chance of occurring. Event B has a 20% chance of occurring. The correlation (i.e. whether they tend to occur together, or separately, or are unrelated) between the events is unknown.

1). What is the maximum probability that both event A and event B will occur?

2). What is the minimum probability that both event A and event B will occur?

Answer 1

Imagine that you are given a random number from 0 to 1. And let's say that the region in red is event A and that in order for this event to happen you will need that number to be from 0 to 0.9, which is 90%. And the region in green is event B, which needs that number to be from 0 to 0.2, which is a 20% chance of happening.

For the best-case scenario, which is to have both these events happening, we need event B to overlap event A. Where the probability of both happening is 20%, from 0 to 0.2.

For the worst case scenario, event B needs to be far away from event A as possible, where the overlap between them is minimal, and they only have a 10% of both happening.