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Section 3-3
The Addition Rule
Addition Rule – “or”
The probability that A or B.One eventMutually Exclusive:
P(A or B) = P(A) + P(B)
Mutually Exclusive events – two events that cannot happen at the same time
What is the probability of rolling a number on a die less than 3 or more than 3?
1
2
4 5
6
2 3
6
5
6833
.
3
Example #1
A golf ball is selected at random from a golf bag. If the golf bag contains 9 Titleists, 8 Maxflis, and 3 Top-flites, find the probability…
a. A golf ball is a Titleist or Maxfli.b. A golf ball is a Maxfli or Top-Flite.c. A golf ball is not a Top-Flite.
Example 2
A standard deck of cards contains 52 cards. One card is randomly selected from the deck. What is the probability..
a. Of randomly selecting a heart or club.
b. Of randomly selecting a 5,6, or 7.
Not Mutually Exclusive – Two events that can happen at the same time, two events that have something in common
What is the probability of rolling a number on a die less than 5 or more than 3?
1 2 4
3
5
6
4 3 1
6
6
6100
.
Mutually Exclusive or
Not Mutually Exclusive?
S = {1,2,3,4,5,6,7,8,9,10,11,12}E = {2,3,4,5,6,7} F = {5,6,7,8,9}G = {9,10,11,12} H = {2,3,4}
1. Are E and F mutually exclusive?2. Are F and G mutually exclusive?3. Are E and G mutually exclusive?4. Are F and H mutually exclusive?
Addition Rule – “or”
The probability that A or B.One eventNot Mutually Exclusive:
P(A or B) = P(A) + P(B) – P(A and B)
Randomly select an individual who is either male or wearing black
NOT mutually exclusive because some (2) of the males are black …
Find the probability of randomly selecting a female or seated.
Find the probability of randomly selecting a female or wearing black.
Roll a Die …
Find the probability of rolling an even number or a number greater than 3.
Find the probability of randomly selecting one person from the Titanic roster, and that person being a man or a boy.
Find the probability of randomly selecting one person from the Titanic roster, and that person being a man or survived.
Find the probability of randomly selecting one person from the Titanic roster, and that person being a woman or survived.
Ticket Issued
No Ticket Issued
Total
Speeding 40 170 210
No Taillights 10 35 45
No Signal 5 25 30
Careless Driving 45 70 115
Total 100 300 400
1. What is the probability that a ticket was issued?
2. What’s the probability a car did not have taillights?
3. What’s the probability a driver will get a ticket, given that they were stopped for careless driving?
4. What the probability a person was stopped for speeding or failure to use signals?
Mixed Practice Ticket Issued
No Ticket Issued
Total
Speeding 40 170 210
No Taillights 10 35 45
No Signal 5 25 30
Careless Driving 45 70 115
Total 100 300 400
5. Given a ticket was not issued, what’s the probability a person was stopped for speeding?
6. What’s the probability that the first person got a speeding ticket and the second person got a ticket for no signal?
Homework:
HW p 136, #15 - 20Quiz tomorrow on conditional probability