CP Algebra II 5/8/15 Name: Addition Rule Warm

CP Algebra II 5/8/15 Addition Rule

Name:________________

Warm-up 1.

Suppose you roll two 6-sided dice. Compute the following probabilities, using area models to explain your answer. a.

P(at least one of the dice is a 5 or a 6)

b.

P(one of the dice is a 4 and the other is not a 3)

2.

Suppose we flip three coins and want to find the probability that you get exactly 2 heads and 1 tail. Can you model this with an area model? Why or why not? How else might you model this problem?

3.

In basketball, a free throw is worth one point. a.

Brian makes free throws with 60% accuracy. (That is, he has a 60% chance of making a free throw). Suppose Brian gets to shoot two free throws. What is the probability that he gets zero points? One point? Two points? Create an area model to help you answer these questions.

b.

Suppose again that Brian gets to shoot two free throws. This time however, if Brian makes the first shot, he will feel more confident, and on his second attempt he will make the shot with 80% probability. If he misses, he will feel less confident, and his second attempt will only have 50% probability of going in. What is the probability he will get zero points? One point? Two points?

Definition: Mutually Exclusive

Example:

16 people study French, 21 study Spanish and there are 30 altogether. Calculate the probabilities of a student selected from this group.

a.

P(Spanish only)

b.

P(French only)

c. 1.

P(BOTH Spanish and French)

Complete the table and use it to determine the each probability.

Sophomore

Brings Lunch 130

Buys Lunch 70

Junior

80

110

Total

a. P(junior) b. P(brings lunch) c. P(sophomore or buys lunch) d. P(junior and buys lunch)

Total

e. P(junior|brings lunch)

2.

Which of the following pairs of events is mutually exclusive? a.

Cards: Aces and Spades

b.

Two dice: Odd and even

c.

Cards: Hearts and Clubs

d.

Two dice: Odd and sum less than 7

3.

A card is chosen at random from a pack of 52 playing cards. What is the probability of a King or a Queen?

4.

A card is chosen at random from a pack of 52 playing cards. What is the probability of an Ace or a black card?

5.

A number is chosen at random from the set of two-digit numbers from 10 to 99 inclusive. What is the probability the number contains at least one “2”?

6.

Two fair dice are thrown. What is the probability that the score on the first die is 6 or the score on the second die is 5?

7.

There are 30 children in a class and they all have at least one cat or dog. 14 children have a cat, 19 children have a dog. What is the probability that a child chosen at random from the class has both a cat and a dog?

8.

In a group of 25 boys, 20 play ice hockey and 17 play baseball. They all play at least one of the games. What is the probability that a boy chosen at random from the class plays ice hockey but not baseball?

9.

In a class of 29 children, 15 like history and 21 like math. They all like at least one of the two subjects. What is the probability that a child chosen at random from the class likes math but not history?

10.

In a class of 32 children, 16 have a skateboard, 12 have a bicycle, and 17 have a scooter. 5 of them have a skateboard and a bicycle. 7 of them have a skateboard and a scooter. 4 of them have a bicycle and a scooter. They all have at least one of the three things. What is the probability that a child chosen at random from the class has a scooter but not a bicycle?

11.

Complete the table and use it to determine the each probability. Runs Track

Plays Water Polo

Total

Boys

18

12

Girls

15

3

Total

CP Algebra II 5/8/15 Name:________________ HW: Addition Rule

a. P(runs track) b. P(girl) c. P(runs track OR girl)

1. What is the probability of scoring a total of 18 when three fair dice are rolled?

d. P(boy AND play water polo) e. P(boy|runs track)

2. Two fair dice, one colored white and one colored red, are thrown. Find the probability that: a.

3.

The score on the red die is 2 or white die is 5.

b.

The score on the white die is 1 or red die is even.

c.

The score on the white die is either 3 or 5.

d.

The score on the white die is either 3 or 5 and the red die is odd.

e.

Both dice show a 4 or 5.

Two sets of cards with a letter on each card as follows are placed into separate bags. Bag 1: I, L, J, A, U

Bag 2: L, R, H, E, C, A

Sara randomly picked one card from each bag. Find the probability that:

4.

a.

She picked the letters ‘J’ and ‘R’.

b.

Both letters are ‘L’.

c.

Both letters are vowels.

A bag contains 9 blue marbles and 3 red marbles. Two marbles are drawn at random. What is the probability of selecting:

5.

a.

Two red marbles?

b.

One red marble and one blue marble?

c.

Two blue marbles?

In a class of 35 children, 22 like bananas, 18 like cherries and 13 like strawberries. 7 of them like bananas and cherries. 8 of them like bananas and strawberries. 5 of them like cherries and strawberries. They all like at least one of the fruits. What is the probability that a child chosen at random from the class likes cherries only?

6.

7.

In a deck of 52 cards, 4 of the cards are Kings. Two cards are randomly picked from the deck. Find the probability of picking: a.

Two Kings

b.

At least one King

c.

Not a King

Complete the table and use it to determine the each probability.

Sophomore

4th period lunch 70

5th period lunch 50

6th period lunch 90

Junior

50

80

70

Total

Total

f.

P(junior)

g. P(5th period lunch) h. P(sophomore or 4th period lunch) i.

P(junior and 6th period lunch)

j.

P(junior|6th period lunch)