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Mutually exclusive union

If we know that event A and event B are mutually exclusive, the probability of either A or B happening is the sum of their probabilities:

this is because the probability of both A and B happening at the same time is zero, so we don’t need to subtract it from the sum of their probabilities like we

Example: rolling a die

Section titled “Example: rolling a die”

If we roll a die, the probability of rolling a 1 is , and the probability of rolling a 2 is also . Because these two events are mutually exclusive, the probability of rolling a 1 or a 2 is .

Example: drawing a card

Section titled “Example: drawing a card”

If we draw a card from a standard deck of 52 playing cards, the probability of drawing a heart is , and the probability of drawing a black card is . Because these two events are mutually exclusive (it’s impossible to pick a black card and a heart, as hearts are red), the probability of drawing a heart or a black card is .