CK-12-Basic Probability and Statistics Concepts - A Full Course

http://www.ck12.org Chapter 1. Independent and Dependent Events

P(AorB) =P(A)+P(B)

P(A∪B) =P(A)+P(B)

P(A∪B) =

15

36

+

3

36

P(A∪B) =

18

36

P(A∪B) =

1

2

P(AandB) = 0

Example C

A card is chosen at random from a standard deck of cards. What is the probability that the card chosen is a diamond
or club? Are these events mutually exclusive?

A standard deck of cards contains 52 cards, with 13 hearts, 13 diamonds, 13 spades, and 13 clubs. Since a card
cannot be a diamond and a club at the same time, choosing a diamond and choosing a club are mutually exclusive
events. Suppose that eventAis choosing a diamond and eventBis choosing a club. The probability that the card
chosen is a diamond or club can then be calculated as follows:

P(A) =

13

52

P(B) =

13

52

P(AorB) =P(A)+P(B)

P(A∪B) =P(A)+P(B)

P(A∪B) =

13

52

+

13

52

P(A∪B) =

26

52

P(A∪B) =

1

2

P(AandB) = 0

Points to Consider

• Can mutually exclusive events be independent? Can they be dependent?

Guided Practice

3 coins are tossed simultaneously. What is the probability of getting 1 or 2 heads? Are these events mutually
exclusive?

Solution:

When tossing 3 coins simultaneously, there are 2^3 =8 possible outcomes. These outcomes are as follows, whereH
represents heads andTrepresents tails: