Name:______
Review for Quiz: Conditional Probabilities, Combinations, Permutations, and Counting Principle
[MM1D2abc] and [MM1D1ab]
COUNTING PRINICPLES
1) You have a choice of vanilla, blueberry, or chocolate ice cream on sugar or regular cone.
How many choices do you have?
2) You toss 3 coins (heads on one side, tails on the other). How many possible outcomes?
3) You have a choice of 5 appetizers, 6 main entrees, and 4 desserts. How many choices do you have?
4) A test consists of 5 true or false questions. How many possible outcomes?
5) A multiple quiz has 12 questions with 4 answers each. How many ways can you complete the quiz?
6) A company uses a four digit employee identification number for its workers.
Workers use their number to gain access to company resources such as photocopiers and restricted areas.
a) How many employee ID numbers are possible if the numbers 0 through 9 are used for each of the 4 digits?
b) Suppose the first digit must be three. Also, the second and third digits cannot be zero.
How many ID codes would be possible in this scenario?
7) You are dining at a buffet-style restaurant. You can choose one meat, one green vegetable, one starch vegetable, and one bread item. According to the menu, you have 3 meats, 3 different green vegetables, 2 starches, and 2 different bread items from which to choose. How many different meals can you make?
8) A reading list contains 11 novels and 5 mysteries. In how many different ways could a student select a
novel or a mystery?
9) A salesperson has 7 customers in Denver and 13 customers in Reno. In how many different ways could
she telephone a customer in Denver or a customer in Reno?
10) Every purchase made on a company’s website is given a randomly generated confirmation code. The
code consists of 4 symbols (letters & digits). How many codes can be generated if at least two letters are
used in each?
II. Permutations & Combinations
Evaluate. Show all of your work.
11) 5! 12) 7P4 13) 4C3
14) Find the number of combinations of 12 objects taken 5 at a time.
15) In how many ways can we arrange the letters in the word COMPUTER? (combination or permutation?)
16) Myra has 6 novels to arrange on a bookshelf. How many ways can she arrange the novels? (combination or permutation?)
17) You want to order a pizza at the local pizza joint. You have enough money to choose 3 toppings from a list of 6 toppings that are offered by the restaurant. How many combinations of toppings are possible? (combination or permutation?)
18) A baseball team has 25 players on its roster. How many ways are there to pick the nine starters for specific positions? (combination or permutation?)
19) Keri wants an ice cream cone with one scoop of chocolate, one scoop of vanilla, and one scoop of strawberry. How many way can the scoops be arranged on the cone? (combination or permutation?)
20) How many pairs of students can Mrs. Grizzle choose to go the math lab if she has 26 students in her class?
(combination or permutation?)
21) The track team is running the relay race in a competition this weekend. There are 14 members of the track team. The relay requires 4 runners. How many ways can 4 runners be formed from the track team?
(combination or permutation?)
22) Kerri got to pick 2 prizes from a grab bag containing 12 prizes. How many different ways can she pick 2 prizes? (combination or permutation?)
23) Terry’s CD player holds 5 CDs. Terry owns 12 CDs. How many different ways can be arrange his CDs in the CD player? (combination or permutation?)
PROBABILITY
24) There are 5 yellow, 4 green, and 2 blue marbles in a hat. Marbles are not replaced. Find P (blue, blue).
25) A deck of cards has 3 yellow, 3 gray, 4 blue, 4 pink, 2 orange cards. Two cards are picked & not replaced.
Find P (yellow, not yellow).
26) There are 6 red, 2 yellow, 6 black, and 5 gray marbles in a hat. Marbles are not replaced. Find P (red, black).
27) You roll a number cube numbered from 1 to 6. You then spin a spinner with 3 sections each with a different color. The spinner has the colors orange, gray, and pink. Find P (2 or 3, orange).
28) You roll a cube which has the numbers 13, 7, 8, 11, 8, and 13 on it. You then spin a spinner which has 8 sections. The letters on the spinner are G, H, E, G, H, C, E, and E. Find P (13, H)
29) Two cards are chosen at random from a deck. Find P (diamond & then a black jack) without replacement.
30) A group has 13 boys 16 girls. If two students are chosen, what is the probability of choosing two girls sequentially?
More Probability J
31) You have a bag of 3 red marbles, 5 blue marbles, and 6 green marbles, find the probability of drawing a green marble GIVEN that one green marble has already been chosen.
32) Two dice are rolled and the sum is recorded. Find the following probabilities. (Tip: Draw a table of sums)
a) P (sum = 8) b) P (sum = 5 or 11) c) P (sum < 12)
Use the spinner to the right to answer the following questions.
Assuming you spin the spinner twice, answer the following questions.
33) P (sum of $200)
34) P (sum of at least $800) 35) P (sum of $400 | 1st spin lands on $200)
36) There are 24 marbles in a bag. Eight are blue, seven are red, and nine are green. If a marble is drawn from the bag and NOT replaced, and then another marble is drawn, find the following probabilities. What is the probability that you draw a blue marble AND then a red OR green marble. P (blue, red or green)