# Human Nature, Biology, and Social Structure: A Critical Look at WhatScience Can Tell Us About Society

## An Introduction to Mathematical Probability

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## Mutually Exclusive Events

The probability of one or the other of two mutually exclusive events happening is the sum of the separate probabilities of these events. If X and Y represent two mutually exclusive events

P(X or Y) = P(X) + P(Y)

This is known as the addition theorem and may be extended to any number of mutually eXclusive events.

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Example 1:
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If a bag contains four blue marbles, six yellow marbles, and five green marbles, what is the probability that in one drawing a person will pick either a blue marble or a green marble?

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Solution:
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There are fifteen marbles in the bag. The probability that a blue marble will be selected is 4/15. The probability that a green marble will be drawn is 5/15 or 1/3.

P(B or G)—P(B) + P(G) = 4/15 + 5/15 = 9/15 = 3/5

The probability that either a blue marble or a green marble will be drawn is 3/5.

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Example 2:
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If a die is thrown, what is the probability that either a two or a six will come up?

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Solution:
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The die can come up any one of six ways. The probability that a two will come up is 1/6. The probability that a six will come up is 1/6.

P(2 or 6) = P(2) + P(6) = 1/6 + 1/6 = 2/6 = 1/3

The probability that either a two or a six will come up is 1/3.

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Exercises:
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- 1.) Are the following pairs of events mutually exclusive?
- ____ a.) Living in New Haven and working in New York.
- ____ b.) Being a freshman and being a junior in high school.
- ____ c.) Being a professor and being an author of a book.
- ____ d.) Drawing a red card and drawing the ace of spades.
- ____ e.) Drawing a face card and drawing the six of hearts from a normal deck of cards.
- 2.) If the probabilities that Joan, Beverly and Evelyn will be elected secretary of a ski club are 1/8, 2/5, and 1/3 respectively, find the probability that one of the three will be elected.
- 3.) If the probabilities that John and Harry will be valedictorian of a high school class are 1/4 and 3/7 respectively, what is the probability that either John or Harry will be valedictorian?
- 4.) Chris and Janet are among twenty girls who enter a tennis tournament. What is the probability that either one of these two girls will win the tournament?
- 5.) In a drawer are six white gloves, four black gloves, and eight brown gloves. If a glove is picked at random, what is the probability that it will be either white or brown?