Imagine for example you want to compute the probability

Imagine for example you want to compute the probability that a pedestrian will be hit by a car while crossing the road at a pedestrian crossing. Let H be a discrete random variable describing the probability of being hit by a car while walking over the crossing, taking one value from { hit, not hit }. Let L be a discrete random variable describing the probability of the cross traffic's traffic light state at a given moment, taking one from { red, yellow, green }.
Realistically, H will be dependent on L. That is, P(H = hit) and P(H = not hit) will take different values depending on whether L is red, yellow or green. You are, for example, far more likely to be hit by a car if you try to cross while the lights for cross traffic are green than if they are red. In other words, for any given possible pair of values for H and L, you must feed them into the joint probability distribution of H and L to find the probability of that pair of events occurring together.


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