Statistics, Test 1

Name: ______________________________________

Problems: 10 points each.

1. Draw a tree diagram for the situation in which:
   For your first course, you can have soup or a salad.
   For your second course, you can have beef, chicken, or pasta.
   For your third course, you can have cake or ice cream.
   What is the number of total possible dinners you can have?
   
   
   
   
   
   
   
2. You are choosing 4 class representatives from a class of 12 people.
   Show how to set up this problem using the first equation on pg. 23.
   What are the total possible combinations of four reps?
   
   
   
   
   
   
   
3. You want to establish a code to pass notes to your friends in class and mention other people.
   You decide to use permutations of their names, so that you can write "Joe" as "Oje."
   One of your classmates is called Lucy, but also Lulu.
   Show the possible combinations for each name.
   Do all combinations, treating each letter as unique,
   then cross out any duplicates, showing why "Lucy" gives us more combinations.
   
   
   
   
   
   
   
   
   
4. There are 8 applicants for the job of cashier at your supermarket. You have 5 cashier positions open.
   Show how to set up this problem using the second equation on pg. 23.
   What are the total possible combinations of 5 cashiers?
   
   
   
   
   
   
   
5. For your trip home from SJC, you first can choose to get to Grand Army Plaza by bus, by subway, or by cab.
   From there, you walk two blocks to get either a bus or a subway.
   You get out at your stop, and then you can either walk home or rent a CitiBike.
   Draw a tree diagram for this situation.
   What are the total number of routes home open to you?
   
   
   
   
   
   
   

Multiple Choice: 5 points each.

1. Imagine a multiple choice test with five questions, each with four answers.
   What are the odds that two students guessing randomly will turn in the exact same test?
   (By same test, I mean each answer is identical.)
   1. 1 in 5
   2. 1 in 4
   3. 1 in 1024
   4. 1 in a million
2. If you have a fair, 12-sided die, what are the chances of rolling a seven?
   1. 1 in 7
   2. 1 in 12
   3. 1 in 6
   4. No one can say
3. Let's say the odds of someone in your building winning the lottery are one in a million.
   Your neighbor wins the lottery today.
   What are your odds of winning it tomorrow?
   1. One in a trillion (1/1000000 * 1/1000000)
   2. Very good: your building is on a lucky streak.
   3. Very bad: your building won't be "due" again for a while.
   4. One in a million
4. Your friend is usually only sick once a year.
   She is sick today. What are the odds that she will be sick tomorrow?
   1. 1 in 365
   2. 1 in 2
   3. Can't say: the events are not independent.
   4. 1 in 7
5. When we are selecting items from a group and order matters, that is called a:
   1. permutation
   2. perversion
   3. combination
   4. confrontation
6. When we are selecting items from a group and order does not matter, that is called a:
   1. permutation
   2. perversion
   3. combination
   4. confrontation
7. How many possible permutations are there of the word "statistics"?
   1. 10!
   2. 10! / (3 * 3 * 2)
   3. 10! / (3! * 3! * 2!)
   4. 10 choose 3
8. In a spa, a person can choose Swedish or Thai massage,
   followed by Russian sauna or Finnish sauna,
   followed by a salt scrub or a facial or a manicure or a pedicure.
   How many possible visit plans are there?
   1. 3
   2. 8
   3. 16
   4. 32
9. If a caterer has 8 items on its menu, and the customer can choose any 4,
   to be served one at a time, the number of possible meals is:
   1. 1960
   2. 1680
   3. 40,320
   4. 70
10. If a caterer has 8 items on its menu, and the customer can choose any 4,
    all to be served at once, buffet style, the number of possible meals is:
    1. 1960
    2. 1680
    3. 40,320
    4. 70