8.01Introduction to Probability

Read each question carefully and answer in the space provided.

1.You are watching the weather for the following school day.The meteorologist states there is a 70% chance of rain.Would it be considered to be more or less likely to rain?

2.You have a bag of 18 marbles.There are 3 red marbles, 2 green marbles, and 13 white marbles.If you were to reach in the bag, would it be more or less likely that you will pull out a red marble?

3.You have a bag of 18 marbles.There are 3 red marbles, 2 green marbles, and 13 white marbles.If you were to reach in the bag, would it be more or less likely that you will pull out a white marble?

In the above diagram, you see a standard deck of cards.Answer each of the following questions using this deck of cards.

4.What is the number of possible outcomes for a deck of cards?

5.What is the probability of randomly drawing a red card?

6.How many Aces are in the deck of cards?

7.Determine the probability of drawing an Ace.

8.Determine he probability of drawing a King.

9.If you were to draw a king from the deck, keep it out of the deck, and then draw a black card, would these two events be independent or dependent?

10.If you were to draw an eight from the deck, return it to the deck, and then draw a queen, would these two events be independent or dependent?

The following table displays the results of the favorite movie genre of freshman students.Use this table to determine the answers to the questions that follow.

Genre of Movie

Number of Students

Horror

27

Action

61

Comedy

73

Romantic

42

Independent

4

11.What is the sample space for the survey?

12.What is the probability that a student's favorite movie is a romantic?

13.What is the probability that a student's favorite movie is a cartoon?

14. What is the probability that a student's favorite movie is an action or comedy?

15. Cole, Madison, and Jaquil won $125 in a "split the pot" at the football game. They divide the winnings three ways but have a problem--$125 can't be divided evenly! As a result, they decide to each take $41 and then play a game to decide who gets the remaining $2. They have two possible methods of deciding who gets the $2, answer the questions about each method.

Method 1:They each take a quarter, shake it up and match heads or tails.The two people who have matching heads or tails will each get $1; the odd person out will receive nothing.If all three coins match, the game continues until only two people have matching heads or tails.

Is this method fair or unfair?

Explain the fairness of the method.

Is this method random or not?

Method 2:They write the numbers 1-10 on slips of paper and take turns drawing the slips from a cup until all the slips have been taken.Next, they get a third person to pick a number 1-10.The person holding that number will receive no money and the other two will each get $1.

Is this method fair or unfair?

Explain the fairness of the method.

Is this method random or not