Mutually Exclusive Events and Overlapping Events

Mutually exclusive events - probabilty theory

Exhibit 33.3 Mutually exclusive events.

As shown in Exhibit 33.3, the events picking a queen (Q) and picking a king (K) are mutually exclusive; their range of possible values do not overlap. For such mutually exclusive events, the probability that either one or the other will occur, is a summation of their individual probabilities:

$$P(Q \,or \,K) = P(Q) + P(K)$$

The probability that the card is either a queen or a king is 4/52 + 4/52 = 8/52.

Events that are not mutually exclusive - probabilty theory

Exhibit 33.4 Events that are not mutually exclusive.

If Q and H are not mutually exclusive events, their range of possible values will overlap as shown in Exhibit 33.4, and the probability that either will occur is:

$$P(Q \,or \,H) = P(Q) + P(H) - P (Q \,and \,H)$$

The probability that the card is either a queen or a heart is 4/52 + 13/52 – 1/52.

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