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1) What does it mean for two outcomes to be mutually exclusive?
2) Give an example of two outcomes from a situation in which the two outcomes are mutually exclusive.
3) Give an example of two outcomes from a situation that are not mutually exclusive.
4) Consider each event. Decide whether each pair of outcomes are mutually exclusive.
a) Roll a die: Get an even number and get a number less than 3.
b) Roll a die: Get a prime number (2, 3, or 5) and get a six.
c) Roll a die: Get a number greater than 3 and get a number less than 3.
d) Select a student: Get a student with blue eyes and get a student with blond hair.
e) Select a college student: Get a sophomore and get a student that is a math major.
f) Select a course: Get an Algebra course and get an English course.
g) Select a voter: Get a Republican and get a Democrat.
5) There are 200 male students at a particular school. Of these, 58 play football, 40 play basketball, and 8 play both.
a) Draw and label a Venn diagram for this situation.
b) How many play both sports.
c) How many play basketball but not football?
d) How many play football but not basketball?
e) How many do not play football or basketball?
6) An architectural firm is putting out bids to design two large governmental buildings. Suppose they believe they have 35% chance of getting the contract for the first building, an 80% chance of getting the contract for the second building and a 10% chance of getting neither job.
a) Draw a Venn diagram for this situation and use your diagram to find the chance that they get both contracts.
b) Use a formula for this situation to find the chance that they get both contracts.
7) A single card from a standard deck can have many descriptions. For example, the King of Spades could be described as a black card, a face card, a king, or a spade. Suppose we pull a single card out of a deck and we pay attention to the outcomes of getting a red card, getting a jack, and getting a spade.
a) Draw a Venn diagram to illustrate this situation paying attention to whether or not it is red, a jack, or a spade.
b) Shade the portion of your diagram with vertical lines that represents the intersection of getting a red card and getting a jack.
c) Shade the portion of the diagram with horizontal lines that represents the union of getting a jack or getting a spade.
8) A student tells their teacher that they want to build a cabinet in wood shop. Students sometimes build this project with oak only, sometimes with cherry only, sometimes with both and sometimes with neither. There is a 40% chance the project will be built using oak, a 50% chance the project will be built using cherry, and a 30% chance that the project will be built using both types of wood. What is the chance that the student will not use either oak or cherry?
[Figure12]
9) Consider a set of 15 pool balls. Balls numbered 1 through 8 are solid and balls 9 through 15 are striped. Suppose the balls are placed into a bag and one ball is randomly selected. Find the probability that:
a) you selected either a solid ball or a ball numbered greater than 12?
b) you selected an even numbered ball or a solid ball?
c) you selected a solid ball or a striped ball?
d) you selected a ball that was striped and even?
10) Suppose you again have a standard set of 15 pool balls. This time, you pull two pool balls out of the bag, replacing the first ball before you select the second ball. What is the probability that:
a) your two pool balls are both solid?
b) you pick exactly the same ball twice?
c) your first ball was solid and your second was odd?
11) At a particular school, there are 20 teachers. Three of them teach math, 5 teach science, and 3 teach computer science. It turns out that there is one teacher who teaches all three classes and one teacher who teaches both science and computer science. Draw a Venn diagram to illustrate the situation and determine how many of the 20 teachers teach courses other than math, science, or computer science. Hint: You will need 3 circles to build this diagram.
Review Exercises
12) Two cards are selected from a standard deck of 52 cards, one after the other without replacement. What is the probability that the two cards are both face cards?
13) Suppose 90% of all Americans have attended a religious ceremony at least one time in the past year. What is the probability that 4 randomly selected Americans will all have attended at least one religious ceremony in the past year?
[Figure13]
14) A single 6-sided die is rolled once and a single card is drawn from a standard deck of 52 cards. What is the probability that the die shows a result greater than 3 and the card is a heart?
15) A young girl has a box of 8 color crayons but has decided they need only 3 colors to make a picture for her grandfather. In how many ways can the child select the three crayons?
16) In how many ways can a committee of 4 people be selected if there must be at least 1 man and 1 women on the committee and there are 6 men and 7 women from which to pick?
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