Question

Give a realistic real life example of 2 binary variables that would be mutually exclusive, or disjoint. Make up the proportions for each variable on their own and prove they are mutually exclusive, or disjoint.

Answer 1

An example of disjoint events is heading north and heading south. Since going north and south, which are in two opposite directions at the same time is not possible, this event is mutually exclusive or disjoint.

The probability for two disjoint events happening at the same time is zero. This can be written as "P(C and D) = 0", where C and D are two different events. The probability of either one of them happening is the summation of both the events' probabilities. It can be written as "P(C or D) = P(C) + P(D)."

Nonmutually exclusive events have some common results. The probability of either one of them happening can be written as "P(C or D) = P(C) + P(D) - P(C and D)."