Union of non disjoint events in simple words

The union of non-disjoint events is the combination of two or more events that can happen at the same time. Non-disjoint events are also called overlapping events or dependent events.

For example, let's say you are playing a game where you draw a card from a deck of cards. The non-disjoint events in this case are drawing a red card or a face card (such as a Jack, Queen, or King). If you draw a red face card, it is both a red card and a face card at the same time.

The union of these non-disjoint events would be written as A ∪ B, where A is drawing a red card and B is drawing a face card. This represents the combination of these two events, or the probability of drawing either a red card or a face card.

The probability of the union of non-disjoint events is calculated using the following formula:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

where P(A) is the probability of event A, P(B) is the probability of event B, and P(A ∩ B) is the probability of the intersection of events A and B (the probability of both events occurring at the same time).

For example, let's say you are trying to predict the outcome of a game of chance, such as rolling a die. The non-disjoint events in this case are rolling an odd number (1, 3, 5) or rolling a number less than 4 (1, 2, 3). If you want to know the probability of rolling an odd number or a number less than 4, the union of these non-disjoint events would be written as A ∪ B, where A is rolling an odd number and B is rolling a number less than 4. The probability of rolling an odd number or a number less than 4 is:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 3/6 + 3/6 - 2/6 = 4/6 = 2/3

So, the probability of rolling an odd number or a number less than 4 is 2/3, or about 67%.

It's important to note that this formula is only valid for non-disjoint events, or events that can happen at the same time.