Discrete Math Quiz: Probability



Review: Probabilty Name:_____________________

I. Describe the Sample Space for each of these Random Experiments. Your answer should be in Brackets like this { } and you should list every possibility!

1) A coin is tossed three times in a row and we observe on each toss whether it lands on heads or tails

2) a gum ball machine has gumballs of 4 different flavors Cherry (c), grape, (G), lemon (l), and sour apple, (S). When a quarter is put into the machine 2 random gumballs come out.

3) Four names (A, B, C, and D) are written each on a separate slip of paper, put in a hat, and mixed well. The slips are randomly taken out of the hat, one at a time, and names recorded.

II. For the following Questions, find the number of possibilities using the Multiplication Rule.

4) A Virginia Licence Plate has 2 letters, followed by three one-digit numbers (0-9).

a) How many combinations are possible for a VA licence plate if repetition is allowed?

b) How many combinations are possible if the first letter must be J and the last number must be 5 (repetition allowed)?

c) How many combinations are possible if no letters or numbers can be repeated?

5) PVHS is having SCA elections. A President, VP, Secretary, and Treasurer must be selected. There are 10 candidates. 6 are female and 4 are male. No one person may hold two positions.

a) How many combinations are possible for filling the positions?

b) How many combinations are possible if the President is female?

c) How many combinations are possible if the President and VP are male and the Secretary and Treasurer are female?

6) A French restaurant offers a menu consisting of 3 different appetizers, 2 different soups, 4 different salads, 9 different main courses, and 5 different desserts.

a) A fixed-price lunch meal consists of a choice of appetizer, salad, and main course. How many different lunch fixed-price meals are possible?

b) A fixed-price dinner meal consists of a choice of appetizer, a choice of soup or salad, a main course, and a dessert. How many

different dinner fixed-price meals are possible?

c) A dinner special consists of a choice of soup, or salad, or both, and a main course. How many dinner specials are possible?

7) Your ID# at UMW must consist of 3 digits (0-9) and 3 letters.

a) How many combinations are possible?

b) How many combinations are possible if the first digit must be 4 and the last letter must be L?

c) How many combinations are possible if no digits or letter are repeated?

8) Your Facebook Password consists of 2 letters followed by 2 digits (0-9). The letters are case sensitive, so a capital letter and a lowercase letter are considered different.

a) How many combinations are possible?

b) How many combinations are possible if no digits are repeated?

c) How many combinations are possible if all the letters are A or a?

III. Probability with Dice. Give all answer as a decimal.

You are rolling one 6- sided die…

9) What is the probability of rolling a 6?

10) What is the probability of rolling a 1?

11) What is the probability of rolling a number greater than 2?

12) What is the probability of NOT rolling a 1?

You are rolling two die… (remember that there are 36 possibilities)

13) What is the probability of rolling a 2?

14) What is the probability of rolling a 4?

15) What is the probability of rolling an 11?

16) What is the probability of rolling an 3 or 4?

IV. Probability with Cards (there are 52 cards in a deck of cards) Give all answers as a decimal.

17) What is the probability of pulling a black card?

18) What is the probability of pulling a Heart?

19) What is the probability of pulling a Jack?

20) What is the probability of pulling a card less than 7? (Aces are low)

21) What is the probability of pulling a 2 or 3?

22) What is the probability of pulling a face card? (no…and Ace is not a face card)

23) Your friend pulls a 6 out of a deck of cards. She does not replace her card. What is the probability of you pulling a 6 from the remaining cards?

24) What is the probability of drawing an 8 and a 10 on two successive draws without replacement?

25) What is the probability of drawing a 5, 6, and 7 on three successive draws without replacement?

26) What is the probability of NOT pulling a 9 or Queen?

Evaluate each of the following:

Permutation Combination

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Directions: For each problem situation, determine if solving the problem requires combinations or permutations, find the numerical value that represents the solution.

1) Elections are being held for student representatives, and next year’s freshman class will determine which two students will be chosen. If five students are running for election, how many different groups of two can be elected to represent the freshman class?

Choose which one this is : _________ combinations _________ permuations

Solve:

2) The new computer desk for your room has enough shelf space to have three reference books. Your parents purchased a set of four reference books for you. How many different ways can you place three of the reference books on the shelf of your new desk?

Choose which one this is : _________ combinations _________ permuations

Solve:

3) Monograms are traditionally written with your last initial in middle surrounded by your first and middle initials. For example, your name is Chris Jordan Smith, then your monogram would be written would be written as follows: .

If you wanted to ignore tradition, how many different ways could you arrange the letters for your monogram if your name was Chris Jordan Smith?

Choose which one this is : _________ combinations _________ permuations

Solve:

4) Your birthday is coming up and you are having a pizza party. You and your friends love to eat pizza and you all enjoy trying pizzas with different toppings. Your favorite pizza parlor only offers 5 toppings nad your budget for the party will allow you to purchase pizzas with only 3 toppings. If no pizza can have one topping twice, how many three-topping pizzas do you and your friends have to choose from?

Choose which one this is : _________ combinations _________ permuations

Solve:

5) There are five finalists in the Mr. Rock Hill pageant. In how many ways may the judges choose a winner and a first runner-up?

Choose which one this is : _________ combinations _________ permuations

Solve:

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