Mutually Exclusive Events

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Mutually Exclusive Events

An Introduction to….

Presentation transcript:

Mutually Exclusive Events

Hipster Venn Diagram

What if… We wanted the probability of event A happening OR event B happening? To answer this we first must define a few things

Mutually exclusive events are… two events that have NO COMMON ELEMENTS (they cannot both occur at the same time). Examples: Drawing an ace, or a face card Rolling doubles, or a total of 7 on two dice Key terms: or, no common element

Mutually Exclusive Events (A Visual)

To find P(A U B) for two mutually exclusive events A and B… you ADD the probabilities P(AUB) = P(A) + P(B)

Mutually Exclusive Example A pair of dice is rolled. What is the probability that the sum of the numbers rolled is either 7 OR 11?

Non-Mutually Exclusive Events Two events, A and B are Not Mutually Exclusive, if they share a common element. Examples: Drawing a king or a face card Rolling doubles or a total of 10 with some dice

Non-Mutually Exclusive Events The probability P(AUB) of non-mutually exclusive events is given by… P(AUB) = P(A) + P(B) – P(A∩B) But why subtract the intersection?

Non-Mutually Exclusive Events (A Visual) The intersection is added TWICE because of the overlap. So we subtract it ONCE. P(AUB) = P(A) + P(B) – P(A∩B)

Non-Mutually Exclusive Example A pair of dice is rolled. What is the probability doubles are rolled OR a total of 10 is rolled?

Homework P. 42 #1 - 7, 9a, 10, 11, 14