Problem A-16

• If Set X = {13,19,22,26,37} and Set Y = {8,19,37,44,103}, what is the intersection of sets x and y?

Problem A-17

• Simplify:• 15x + 3y – 6x + 3 + 5y =

Problem A-18

• For sets R and S, determine the value R ∩ S.

• R = {-4,-1,2,3,5}• S = {1,2,3,4,5,6}

Problem A-19

• Name the coefficients, constant terms, and like terms of the expression:

• 3x + 2 – 5x -7

Problem A-20

• What is a disjoint set?

Problem A-21

Billy has 3 red marbles, 5 white marbles, and 4 blue marbles on the floor. His cat comes along and bats

one marble under the chair. What is the probability it is a red marble?

Problem A-22

• There are 15 candy-coated chocolate pieces in a bag. 3 have defects in the coating that can be seen only with close inspection. What is the probability of pulling out a defective piece without looking?

Problem A-23

An umpire at a little league baseball game has 14 balls in his pockets. Five of the balls are brand A, 6 are brand B, and

3 are brand C. What is the probability that the next ball he throws to the

pitcher is a brand C ball?

Problem A-24

Terrell casts his line into a pond containing 7 catfish, 8 bream, 3 trout, and 6 northern pike. He immediately catches a bream. What are the chances that Terrell will catch a second bream when he casts his line again?

Find the probability of tossing a coin and getting tails and rolling a

number cube and getting a number less than 5.

Problem A-25

In how many different ways can Sarah line up 4 different books on a

shelf?

Problem A-26

Three runners are in a race. If they all finish at different times, in how many ways can they finish the race

in first, second, and third place?

Problem A-27

There are 10 balls in a box, each with a different digit on it: 0,1,2,3,4,5,6,7,8, & 9.A ball is chosen at random and then put back in the box. What is the probability that if you picked out a ball 3 times, you

would get number 7 each time?

Problem A-28

You are playing a children’s board game with your little brother. You are five spaces away from a red space (lose a turn) and 11 spaces away from an orange space (give a token to the opponent). What are your chances of rolling two fair dice and losing your turn or having to give a token to your brother on your next roll?

Problem A-30

Problem A-31

Jamal is considering playing a game with his neighbors, Gary and Mark. They will take turns tossing two fair coins. Jamal will get a point if they are both heads. Gary will get a point if they are a head and a tail. Mark will get a point if they are both tails. Players continue playing until a player reaches

10 points. Is this a fair game?

A can of paint is mislabeled at the plant. It could be green, pink, or

yellow. Based on production, there is a 20% chance that it is green and a 40% chance it is pink. What is the

chance it is yellow?

Problem A-32

Suzie recorded the color of each car driving by her house this week and obtained the following information. Based on her table, estimate the probability that the next car to drive by will be white or tan.

Problem A-33

Black White Tan Other 75 63 102 85

You toss a coin three times. You can get 0, 1, 2, or 3 heads.

Are these four events equally likely? Why or why not? Calculate the

probability of each event.

Problem A-37

What are your chances of landing on 4 on the spinner or tossing a fair coin and getting tails?

Problem A-38

1

2 3

4

Warm-Up A-39

• A pair of number cubes is tossed. What is the probability of getting a sum of 3 or less?

Answer A-16

• X ∩ Y = {19,37}

Answer A-17

• 9x + 8y + 3

Answer A-18

• R ∩ S = {2,3,5}

Answer A-19

• Coefficients: 3, 5• Constant terms: 2, -7• Like Terms: 3x, -5x• 2, -7

Answer A-20

• A set that contains no elements in common.

Answer A-21

3/12 3/12 = ¼

Expressed as a decimal 0.25Expressed as a percent 25%

Answer A-22

• 3/15 = 1/5• Expressed as a decimal 0.20• Expressed as a percent 20%

Answer A-23

•21%•3/14 because there are 3

C balls and 14 total balls. 3/14 = o.214 which rounds to 0.21 or 21%

ANSWER A-24

Because there were only 7 bream left and only 23 fish left to catch.

Answer A-25

• P(tails) = favorable = 1• possible 2

• P(<5) = favorable = 4 = 2• possible 6 3• Multiply the two probabilities:• 1 X 2 = 2 = 1• 2 3 6 3

Answer A-26

• Permutation – Find the factorial.• Use an exclamation point to denote the

permutation.• 4! = 4 x 3 x 2 x 1 = 24• There are 24 different ways to line up the

books on the bookshelf.

Answer A-27

• 3! = 3 x 2 x 1 = 6

Answer A-28

• Multiply the chances together.• 1/10 x 1/10 x 1/10 = 1/1000

• You have 1 in 1000 chances of picking the 7 ball 3 different times.

• *Remember the ball was replaced each time in this situation.

Answer A-30

Your sample space consists of 36 equally likely outcomes:

{(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}

Answer A-30, cont.

Probability for either of two mutually exclusive events A or B is the sum of the two probabilities. Thus,

P(5 or 11) = P(5) + P(11)

= = =

Answer A-31The sample space consists of four equally likely

outcomes: {HH, HT, TH, TT}

The probability of a player winning is calculated by

dividing the number of winning outcomes by the total number of possible outcomes. Thus,

P(Jamal wins) = P(HH) =

Answer A-31, cont.

and P(Mark wins) = P(TT) =

but…

P(Gary wins) = P(HT or TH) =

A fair game is one in which all players are equally likely to win. NO FAIR!

Answer A-32

The probabilities of all possible outcomes in the sample space must add up to 100%. Therefore,

P(green) + P(pink) + P(yellow) = 100% 40% + 20% + P(yellow) = 100%

60% + P(yellow) = 100%

60% - 60% + P(yellow) = 100% - 60% P(yellow) = 40%

Answer A-33

• The total number of cars for the week was 325, and of those, 63 were white. Thus, the probability of having a white car drive by next is:

• P(white) =

Similarly,• P(tan) =

Answer A-33 Con’t

• P(white or tan) = P(white) +P(tan)• = 0.194 + 0.314 = 0.508 = 50.8% or 51%

Another way to calculate this: P(white or tan) =

Answer to A-35:The Fundamental Counting

Principle states that if there are m ways to do one thing and n ways to do another after the first is done

and p ways to do a third, etc., then there are m x n x p… ways to do

them all. So…

Answer to A-35, cont. There are 26 letters to choose from for the first 3 slots and 10 digits to choose from for the last 3 slots.___ ____ ____ ____ ____ _____ 26 26 26 10 10 10 So the total number of unique plates possible is: 26 x 26 x 26 x 10 x 10 x 10 = 17,567,000 different plates.

Answer A-37Outcomes for each event are:0 Heads: TTT 1 outcome1 Heads: HTT, THT, TTH 3 outcomes2 Heads: HHT, HTH, THH 3 outcomes3 Heads: HHH 1 outcome

Total outcomes are 8

Answer A-37, cont.

Therefore, P(0 Heads) = 1/8 = 0.125 = 12.5%

P(1 Heads) = 3/8 = 0.375 = 37.5% P(2 Heads) = 3/8 = 0.375 = 37.5% P(3 Heads) = 1/8 = 0.125 = 12.5%

They are NOT equally likely.

Answer A-38

P(4) = ¼ = 0.25 = 25%P(T) = ½ = 0.50 = 50%

P(4 or T) = P(4) + P(T) = ¼ + ½ = ¼ + 2/4 = ¾

= 0.75 = 75%.

Answer to A-39

P(2 or 3) = P(2) + P(3) Referring to a 2-dice sum chart,

this equals: 1/36 + 2/36 =3/36 = 1/12 = 0.083 = 8.3% = 8%