Probability of Compound Events

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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