The Addition RuleThe Addition Rule The Addition RuleThe Addition Rule

Chapter 3.3Chapter 3.3

Objectives• Determine if 2 events are mutually

exclusive• Use the Addition Rule to find the

probability of 2 events

Mutually Exclusive Events• Two events are mutually

exclusive if A and B cannot occur at the same time.

A AB B

Are these events mutually exclusive?

• Event A: Roll a 3 on a die• Event B: Roll a 4 on a die• yes

Are these events mutually exclusive?

• Event A: Randomly select a male student

• Event B: Randomly select an Auto Tech student

• No, a student can be both male and in Auto Tech

Are these events mutually exclusive?

• Event A: Randomly select a blood donor with type O blood.

• Event B: Randomly select a female blood donor

• No, a blood donor can be both female and type O

• What is the probability of rolling a 3 or a 4 on a 6-sided die?

The Addition Rule• The probability that events A or B

will occur P(A or B) is given by• P(A or B) = P(A) + P(B) – P(A-B)• If events A and B are mutually

exclusive, then the rule can be simplified to

• P(A or B) = P(A) + P(B)

Find the probability . . .• Of selecting a card from a

standard deck that is a 4 or an ace . . .

• P(4 or ace) = P(4) + P(ace)• = 4/52 + 4/52 = 8/52 = 2/13

= .154

Find the probability . . .• Of rolling a number less than 3 or

an odd number . . .• These events are not mutually

exclusive• P(less than 3 or odd) = P(less than

3) + P(odd) – P(less than 3 and odd)• = 2/6 + 3/6 – 1/6 = 4/6 = 2/3

= .667

Sales Volumes• This chart shows

the volume of sales (in dollars) and the number of months a sales rep reached sales level during the past 3 years.

Sales Volume Months

0-24,999 3

25,000-49,999 5

50,000-74,999 6

75,000–99,999 7

100,000-124,999 9

125,000-149,999 2

150,000-174,999 3

175,000-199,999 1

Sales Volumes• If this sales

pattern continues, what is the probability that the sales rep will sell between $75,000 and $124,999 next month?

Sales Volume Months

0-24,999 3

25,000-49,999 5

50,000-74,999 6

75,000–99,999 7

100,000-124,999 9

125,000-149,999 2

150,000-174,999 3

175,000-199,999 1

Sales Volumes• A = sales between

75,000 & 99,999• B = sales between

100,000 & 124,999• P(A or B)=P(A)

+P(B)• = 7/36 + 9/36 • =16/36 =4/9 =.444

Sales Volume Months

0-24,999 3

25,000-49,999 5

50,000-74,999 6

75,000–99,999 7

100,000-124,999 9

125,000-149,999 2

150,000-174,999 3

175,000-199,999 1

•In a survey conducted by the National Family Organization, new mothers were asked to rate the difficulty of delivering their first child compared with what they expected.•If you selected a new mother at random and asked her to compare the difficulty of her delivery with what she expected, what is the probability that she would say that it was the same or more difficult than what she expected?

Example 5, p. 144• Use the graph on p. 144 to find the

probability that a randomly selected draft pick is not a running back or a wide receiver.

• Define A: Draft pick = running back• Define B: Draft pick = wide receiver• P(A or B) =19/255 + 32/255 =51/255 = 1/5• P(not RB or WR) = 1 – 1/5 = 4/5 = .8

Turn to page 145• Do questions 1-9, 19 together• Homework: 10-24 evens