Advanced Algebra

Probability Review

1.

• Use a standard deck of cards (with no jokers) for the following:

• P(face card)

3Answer:

13

2.

• Use a standard deck of cards (with no jokers) for the following:

• P(diamond or 7)

4Answer:

13

3.

• Use a standard deck of cards (with no jokers) for the following:

• P(not black)

1Answer:

2

4.

• Use a standard deck of cards (with no jokers) for the following:

• P(14)

Answer: 0

5.

• Evaluate (must show work!)• 11P9

11!

Answer: 19,958,40011 9 !

6.

• Evaluate (must show work!)• 7C2

7!

Answer: 212! 7 2 !

7.

• In a race there are 12 runners. How many ways can first, second, and third place be determined?

12 3Answer: 1320 waysP

8.

• A track coach has ten players trying out for four spots on a relay team. How many ways can the coach determine the relay?

• Bonus question: If it is important to select one runner to be the one to start out of the blocks, how many ways could the coach choose the relay now?

10 4Answer: C 210 ways

10 1 9 3Answer: 840 waysP C

9.• Among other accessories, the

original Mr. Potato Head comes with 5 pairs of eyes, 2 sets of teeth, 4 mouths, 2 tongues, 4 noses, and 3 mustaches

• Note that you may only have one mouth, teeth, or tongue at a time

• How many possible ways could you make Mr. Potato Head’s face if you fill every spot each time (with the correct body parts)?Answer: 5 8 4 3 480 ways

10.

• How many five letter permutations can be formed from the letters SILVERHAWK?

10 5Answer: 30,240 waysP

11.

• You are making a sandwich. You have five options for the bread, eight options for the meat, four options for vegetables, and six options for the spreads. Your sandwich only has space for one type of bread, one type of meat, two vegetables, and two spreads. How many possible different sandwiches could you make?

5 1 8 1 4 2 6 2Answer: C 3600 sandwichesC C C

12.

• Classify as independent or dependent, then find the probability.

• A standard number cube is rolled and a card is pulled from a standard playing deck (no jokers). Find the probability of rolling less than or equal to three and drawing a red face card

3 6 3Answer: Independent,

6 52 52

13.

• Classify as independent or dependent, then find the probability.

• You have twelve spoons, fourteen forks, and ten knives in a bag. Assuming the probability of grabbing a utensil without looking it is equal for all three types, what is the probability of removing a spoon for you and a friend in a row?

12 11 11Answer: Dependent,

36 35 105

14.

• Determine if it is mutually exclusive or not, then find the probability.

• In a certain school 28% of the students are in a differentiated class and 19% of the students are in an AP class. If 61% of the students are not in a differentiated or AP class, determine the probability that a random student is in a differentiated and an AP class.

Answer: Not M.E., 8%

15.

• Determine if it is mutually exclusive or not, then find the probability.

• What is the probability that if you roll two dice that their sum will be odd or a prime number?

19Answer: Not M.E.,

36(2) (3) (5) (7) (9) (11)

1 2 4 6 4 2 19

36 36 36 36 36 36 36

P P P P P P

16.

• Write the binomial expansion for (2x – 1)7

7 6 5 4

3 2

Answer: 128 448 672 560

280 84 14 1

x x x x

x x x

17.

• Find the ninth term in the expansion of(4x + 2)11

3 8 311 8Answer: 4 2 2,703,360C x x

18.

• The first term in a binomial expansion is 243x5 and the second term is –810x4. What is the original binomial and to what power is it raised?

5Answer: 3 2x

19.

• What is the probability of randomly guessing on a ten question multiple-choice quiz with four answers per question and getting at least a C (at least 70%)?

7 3 8 2

10 3 10 2

9 1 10 0

10 1 10 0

Answer:

1 3 1 3

4 4 4 4

1 3 1 3

4 4 4 4

0.35%

C C

C C