# Data Science different topic explanation -- Part-4 -- Disjoint and overlapping events

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# Data Science different topic explanation – Part-4 – Disjoint and overlapping events

Disjoint events cannot happen at the same time. A synonym for this term is “mutually exclusive”.

For instance, the outcome of a single coin toss cannot be head and a tail, it can be either head or tails.

The not disjoint event can happend at the same time. Therefore they can overlap, and the probability of overlapping should be excluded from total probability to avoid double counting.

Example: What is the probability of drawing a Jack or a Red card from a well-shuffled deck of 52 cards?

Several ways it can happen: 4 (there are 4 jacks) and 26 (there are 26 red cards). But there are 2 Red cards overlap between them. Two red jacks that fit both criteria.

Total number of outcomes: 52 (there are 52 cards in total)

So, P (Jack or Red card) = P(Jack) + P(Red card) - P(Jack and Red card) = 4/52 + 26/52 - 2/52 = 7/13