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Addition Rule (Mutually Exclusive Events)

P(A∪B)=P(A)+P(B)P(A \cup B) = P(A) + P(B)

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Mutually exclusive (disjoint) events have no outcomes in common — a single card cannot be both a king and a queen, one die roll cannot be both a 2 and a 5 — so their chances simply add. Drawing one card, P(king or queen) = 4/52 + 4/52 = 8/52 ≈ 0.154. Enter each probability as a decimal from 0 to 1, or switch the unit to % and type 25 instead of 0.25.

Galileo was asked by his Medici patrons why, with three dice, a total of 10 shows up more often than 9 even though both can be made six ways; his short memo Sopra le Scoperte dei Dadi answered it by adding the probabilities of genuinely distinct, equally likely outcomes rather than of the unordered "ways". That is the standing trap: the rule breaks the moment the events can happen together. "Drawing a king" and "drawing a heart" overlap in the king of hearts, so adding them double-counts one card — use the general addition rule for that. A useful sanity check is built in here: if your two exclusive probabilities sum past 1, one of them is wrong.

Addition Rule (Mutually Exclusive Events)
P(A∪B)=P(A)+P(B)P(A \cup B) = P(A) + P(B)
Where
  • P(A∪B)P(A \cup B)= Probability of A or B
  • P(A)P(A)= Probability of A
  • P(B)P(B)= Probability of B
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