Name MAT 143 Lab:Tree Diagrams, Counting Principle, ProbabilityI. Counting Principle

1. You are required to take five courses, one each in humanities, sociology, science, math, and music. You have a choice of four humanities courses, three sociology courses, five science courses, two math courses, and three music courses. How many different sets of five courses are possible?

2. The car model you are considering comes with or without air conditioning, with or without sun roof, with or without CD player, and in eight stock colors. How many different versions of the car are available?

3. A lock consists of a dial that can be set to any of the numbers 1 - 30. How many different three-number combinations are possible if numbers can be repeated?

4. A restaurant has 7 entrees, 6 vegetables, and 9 desserts on its menu. If you want to order a meal consisting of one item from each of these categories, how many possible choices do you have?

II. Tree Diagrams and Probability

5.Two balls are drawn (one after the other) with replacement from a bag containing a red, a blue, & a white ball.

a) Draw a tree diagram and list the sample space.

b) P(drawing at least one white ball) c) P(drawing no white balls) d) P(drawing both blue balls)

6. A coin is flipped and then a die is rolled.

a) Draw a tree diagram and list the sample space.

b) P(obtaining heads and then rolling a 3) c) P(obtaining heads and rolling an even number)

d) P(obtaining tails or rolling an odd number) e) P(obtaining tails or rolling a 4)

7. A couple is planning on having three children.

a) Use the counting principal to determine the number of sample points in the sample space.

b) Draw a tree diagram and list the points in the sample space.

1. P(they have only boys) d) P(the oldest child is a boy and the youngest child is a girl)

e) P(exactly two boys and exactly two girls) f) P(at least two girls).

III. Probability

8. One card is drawn from a standard deck of cards. Find the probability that the card drawn is:

Note: Ace is considered a low/number card and Face cards are Jack, Queen, King

a) A spade or a face card b) A heart or a black ace

c) A red card or a black card d) A red card or an ace

e) Not a number card or is a diamond f) A number card or a face card

g) A number card less than 4 or a 2 h) A red spade

9. In tossing a fair coin 500 times, the results were heads on 280 trials. Find the probability that a coin toss will be heads.

10. At his favorite fishing spot, John Jones caught 24 fish in a single afternoon. 12 of this were bass, 3 were catfish, and the rest were perch. Find the probability that the next fish he catches in this spot will be a

a) bass b) catfish c) perch

11. A special 6-sided die is made with the following symbols:,,,,,. It is rolled once. Find the probability for each of the following events.

a) P() b) P() c) P(not) _________

12. At a certain Chinese restaurant, each customer is offered a plate with 8 fortune cookies on it. In each cookie there is a slip of paper, which gives the customer a discount of $1, $2, or $5 off of the price of his/her meal. There are 5 cookies with a slip for a $1 discount, 2 cookies with a slip for a $2 discount, and 1 cookie with a slip for a $5 discount. A customer is allowed to choose only one cookie. Find the probability that the customer receives each of the following discounts.

a) $1 b) $2 c) $5 d) more than $1

13. One card is drawn from a standard deck of 52 cards. Find the probability that the card is

1. P(a king) b) P(face card) c) P(the ace of diamonds)

d) P(a card with the number 13 printed on it) e) P(not a queen)

f) P(a king or a queen) g) P(a spade or a face card)

14. In a study of 100 people, the data in the following table were obtained:

Lung cancer No lung cancer

Smoker 45 10

Non-smoker 12 33

One person from this study is picked at random. What is the probability that

a) the person is a smoker b) the person does not have lung cancer

c) the person is a non-smoker and has lung cancer__________

15. If Kara buys various types of drinks for a barbeque and places them in a cooler under ice. If she bought 15 Dr. Peppers, 18 waters, 10 Mountain Dews, and 14 Diet Sprites, find the probability of selecting the following if only one drink is selected at a time:

a) A Dr. Pepper b) Anything except Diet Sprite

c) Mountain Dew or Diet Sprite d) Water and Mountain Dew

answer all question provide work