Chapter 7 Probability

Practice Lessons 1-4And Ch 8 less 6Mrs. Parziale

• A fair coin is flipped three times. Write out all possible outcomes that make up the sample space. Remember, order does matter.

• Save your sample space for the next problem.

Sample Spaces and Outcomes

Sample Spaces and Outcomes

Using the sample space in the previous problem,• Find P(exactly two heads)?

• Find P(at least one head)?

Sums of Two Die

• Using the Sums of Two Die sample space in your notes (or think about it),

• What is the probability of getting a sum of 8?• What is the probability of getting a sum of 7?• What is the probability of getting a sum greater

than 3?• What is the probability of getting a sum that is

even?• What is the probability of getting a sum of 1?

Mutually Exclusive or Not?

• Which sets are mutually exclusive?

A = {1,2,3,4} B = {4,5,6} C = {5, 6}

Which is Which? What’s the Probability?

• Mutually Exclusive or Not Mutually Exclusive–– What is the probability you will roll a sum of 2 or 3?

– What is the probability you will roll a sum of a multiple of 3 or a sum of 6?

– What is the probability you will roll a sum of 4 or 9?

• Fifty girls of the junior class participate on either the swim team or the track team or BOTH teams. Thirty girls swim on the swim team and 42 girls are on the track team. Draw a Venn Diagram that shows how many just swim, just do track, and how many do both.

• How many only play on one of the two teams?

• There are 50 assorted super balls of various colors in a bucket. Thirteen of these are green. What is the probability of selecting a green one?

Multiplication Counting Principle• A restaurant has the menu below. How many different

dinners of 1 entrée, 2 side dishes, 1 beverage, and 1 dessert could a person order? Assume no choice is repeated.

Entrees:• Grilled Chicken• Hamburger Deluxe• Lasagna

Sides:• Mashed Potatoes• French Fries• Apple Sauce• Corn• String beans• Beets

Beverages:• Soda• Milk• Juice

Desserts:• Cheesecake• Jello• Ice Cream• Apple Pie

Without Replacement

• Ben decides to rank order the 5 colleges he has visited. How many rankings can he make?

With Replacement

• Suppose a bag contains 8 numbered balls from 1 to 8. How many ways can you selected 5 balls if each ball is replaced after each selection?

Evaluate

6 4P

15 4P

15 4C

6 4C

Solve

4 35n nP P ! 4 2( 1)!x xx

Combination or Permutation?

• How many different ways can 6 students sitting on a bench be arranged?

• Ben and Jerry are making sundaes for a local youth center. They have 8 toppings the children can choose from to put on their ice-cream. How many different sundaes can be made using 3 toppings.

• Eighteen basketball players are competing for 5 starting positions. The players selected to start will make up the first team. If the order in which the players are selected is not important, how many different teams are possible?

Combination or Permutation?

• Ten golfers are competing in a high school tournament. How many different ways can 3 of the golfers finish first, second, and third?

Combination or Permutation?

Complements

• Given the diagram below, find the probabilities.

20 45

P A B

P A B

( )P A

( )P not BA B

5