Probability of Compound Events Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of...
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Transcript of Probability of Compound Events Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of...
Probability of Compound Events
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Lesson QuizzesLesson Quizzes
Probability of Compound Events
Learn to find probabilities of compound events.
Probability of Compound Events
A pizza parlor offers seven different pizza toppings: pineapple, mushrooms, Canadian bacon, onions, pepperoni, beef, and sausage. What is the probability that a random order for a two-topping pizza includes pepperoni?
Additional Example 1: Using an Organized List to Find Probability
Let p = pineapple, m = mushrooms, c = Canadian bacon, o = onions, pe = pepperoni, b = beef, and s = sausage. Because the order of the toppings does not matter, you can eliminate repeated pairs.
Probability of Compound Events
Pineapple – m Mushroom – p Canadian bacon – p Pineapple – c Mushroom – c Canadian bacon – mPineapple – o Mushroom – o Canadian bacon – oPineapple – pe Mushroom – pe Canadian bacon – pePineapple – b Mushroom – b Canadian bacon – bPineapple – s Mushroom – s Canadian bacon – s
Onions – p Pepperoni –p Beef – p Sausage – p Onions – m Pepperoni – m Beef – m Sausage – m Onions – c Pepperoni – c Beef – c Sausage – c Onions – pe Pepperoni – o Beef – o Sausage – o Onions – b Pepperoni – b Beef – pe Sausage – b Onions – s Pepperoni – s Beef – s Sausage – pe
Continued: Check It Out: Example 1
The probability that a random two-topping order will include
pepperoni is . 27
P (pe) = =6
21
2
7
Probability of Compound Events
Check It Out: Example 1 A pizza parlor offers seven different pizza
toppings: pineapple, mushrooms, Canadian bacon, onions, pepperoni, beef, and sausage. What is the probability that a random order for a two-topping pizza includes onion and sausage?
Let p = pineapple, m = mushrooms, c = Canadian bacon, o = onions, pe = pepperoni, b = beef, and s = sausage. Because the order of the toppings does not matter, you can eliminate repeated pairs.
Probability of Compound Events
Pineapple – m Mushroom – p Canadian bacon – p Pineapple – c Mushroom – c Canadian bacon – mPineapple – o Mushroom – o Canadian bacon – oPineapple – pe Mushroom – pe Canadian bacon – pePineapple – b Mushroom – b Canadian bacon – bPineapple – s Mushroom – s Canadian bacon – s
Onions – p Pepperoni –p Beef – p Sausage – p Onions – m Pepperoni – m Beef – m Sausage – m Onions – c Pepperoni – c Beef – c Sausage – c Onions – pe Pepperoni – o Beef – o Sausage – o Onions – b Pepperoni – b Beef – pe Sausage – b Onions – s Pepperoni – s Beef – s Sausage – pe
P (o & s) =1
21The probability that a random two-topping order will include onions and sausage is .1
21
Continued: Check It Out: Example 1
Probability of Compound Events
Jack, Kate, and Linda line up in random order in the cafeteria. What is the probability that Kate randomly lines up between Jack and Linda?
Additional Example 2: Using a Tree Diagram to Find Probability
Make a tree diagram showing possible line-up orders.Let J = Jack, K = Kate, and L = Linda.
List permutations beginning with Jack.
List permutations beginning with Kate.
List permutations beginning with Linda.
K L = JKL
L K = JLKJ
L J = KLJK
J L = KJL
K J = LKJL
J K = LJK
Probability of Compound Events
Additional Example 2: Continued
The probability that Kate lines up between Jack and
Linda is . 1
3
P (Kate is in the middle)
=Kate lines up in the middle
total number of equally likely line-ups=
2
61
3=
Probability of Compound Events
Jack, Kate, and Linda line up in random order in the cafeteria. What is the probability that Kate randomly lines up last?
Check It Out : Example 2
Make a tree diagram showing possible line-up orders.Let J = Jack, K = Kate, and L = Linda.
List permutations beginning with Jack.
List permutations beginning with Kate.
List permutations beginning with Linda.
K L = JKL
L K = JLKJ
L J = KLJK
J L = KJL
K J = LKJL
J K = LJK
Probability of Compound Events
=P (Kate is last) =Kate lines up last
total number of equally likely line-ups
2
6
1
3=
The probability that Kate lines up last is .1
3
Check It Out : Example 2 (Continued)
Probability of Compound Events
Mika rolls 2 number cubes. What is the probability that the sum of the two numbers will be less than 4?
Additional Example 3: Finding the Probability of Compound Events
There are 3 out of 36 possible outcomes that have a sum less than 4.The probability of rolling a sum less than 4 is .
1
12
Probability of Compound Events
Mika rolls 2 number cubes. What is the probability that the sum of the two numbers will be less than or equal to 4?
Check It Out: Example 3
There are 6 out of 36 possible outcomes that have a sum less than or equal to 4.The probability of rolling a sum less than or equal to 4 is .
1
6