Probability

1. Probability

2. There are 52 cards in a deck. So what are my chances of picking an ace?

3. 4 How many aces are in a deck? 52 How many cards are in a deck? So I have a 4/52 or 1/13 chance of drawing an ace!

4. There are 9 homerooms in the school and 20 students in each homeroom. If the principal selects 3 of the homerooms in no specific order, what is the probability of your room being selected? A. 1/5 B. 1/3 C. 3/20 D. 9/20

5. Jack’s sock drawer contains 10 blue socks and 12 gray socks. The room is dark and he cannot turn on the light. What is the least number of socks he must take out of the drawer to be certain he has a pair of the same color?

6. 3socks …because if the first two do not make a pair, then the third will have to match one of the first two!

7. What does it mean when someone asks you to calculate all the possible outcomes of a problem? An Example:  Anne decided to go out for a Space Burger at the Marsburg Burger Bar. The Burger bar serves a different type of burgers: Jumpers! Burgers come with two of the following toppings: (Or you have to pay extra!) lettuce, tomato, or mushrooms. Anne likes them all!

8. Step 1: The first step you have to do to solve a problem like this is to think, "This is one of those problems where I have to make an organized list, or a chart." Here is why:You have four things to make your possible combinations with. One is always in every group - the Jumping Burger!

9. You are asked to make combinations of three objects: a Jumper + 2 of the toppings pictured above. You could draw pictures to show what is in each group, but that takes a lot of time! Here is a picture showing one possible combination: (Jumper, lettuce, tomato)

10. And then....You have to remember: (Jumper, lettuce, tomato) is the same as (Jumper, tomato, lettuce) , so these two combinations only count as one because they are the same things in a different order. You still have the same two things on your burger...........

11. But, (Jumper, lettuce, tomato) and (Jumper, lettucemushroom) are two different groups of combinations, because they are NOT the same things in a different order. These groups count as two combinations.

12. Jumper = J Lettuce = L Tomato = T Mushroom = M Step 2: The easiest way to start organizing is to make a key for the items you are supposed to combine. Here's an example: (You DON'T have to draw the pictures!)

13. Tomato Lettuce Mushroom J, T, L J, L , T J, M ,T J, T, M J, L M J, M, L Step 3: Next, you make a simple chart and figure out ALL possible combinations.

14. Tomato Lettuce Mushroom J, T, L J, L , T J, M ,T J, T, M J, L M J, M, L Step 4: Finally, you get rid of the "copycat combinations"! (I'm going to color mine blue because I can't cross them out!)

15. Now you have the answer: There are three possible combinations of toppings Anne could have on her Jumper! You can say there are 3 possible outcomes of the problem, "How many possible combinations of 2 toppings could Anne choose from to put on her Jumper Burger?" She will either have aJumper burger with tomato and lettuce, a Jumper burger with tomato and mushrooms, or aJumper burger with lettuce and mushrooms.

16. Have you ever had to figure something like this out? Of course you have! It happens every time you have choices. Usually we just choose our favorite things, so we don't think about all of the possible things we could have had if we made different choices. What are some times you had to make choices?

17. Now You Try One Dairy Queen has a cool new kind of milk shake. You get to choose any two flavors of ice cream from 7 choices, and they put them both in the glass at the same time, so you get a 'half and half' shake. They have vanilla, chocolate, strawberry, peach, mocha, banana, and chocolate mint. What combinations could I get for my 2 flavor milk shake?

18. How many items are we combining? 7 How many items should be listed on our table? 7

19. Make your table and fill in ALL possible choices.

21. Cross out ALL choices that are a repeat. For example, Vanilla-Strawberry is the same as Strawberry-Vanilla.

22. x x x x x x x x x x x x x x x x x x x x x

23. Did you see a pattern? How many choices are there? 21

24. Maria and Cassie were playing a game, and Cassie needed to roll exactly a five to win. Cassie said, "Maria, do you think I should roll both dice or just one? Would I have a better chance of winning if I just rolled one? Maria answered, "I think we can figure it out with math." Help Cassie and Maria figure the probability of Cassie getting a 5 both ways. Maria and Cassie were playing a game, and Cassie needed to roll exactly a five to win. Cassie said, "Maria, do you think I should roll both dice or just one? Would I have a better chance of winning if I just rolled one? Maria answered, "I think we can figure it out with math." Help Cassie and Maria figure the probability of Cassie getting a 5 both ways. or or

25. Advice from the teacher: Look at the possibilities using one die. 1 in 6 Hint: Look at the possibilities of using 1 die. 1 in 6

26. Make a table to help figure out all the combinations of two dice. Sum of 2 Dice 2 3 4 5 6 7 3 4 5 6 7 8 4 5 6 7 8 9 5 6 7 8 9 10 6 7 8 9 10 11 7 8 9 10 11 12 Make a table to find the ways to equal 5 with 2 dice:

27. Type your answers to the following questions then hit the submit button. Answer the following questions to help you find the answer: • How many possible sums are there altogether with 2 dice? There are 6 sides on each die. 6 x 6 = 36 36

28. 2. How many sums of 5 are possible with two dice? 4 3. What is the probability that you will get a sum of 5 when you roll 2 dice? 4 in 36 or 1 in 9 4. So what is the best game-winning strategy? Roll one or two dice when you want to get a 5?   1 1 in 6 is better than 1 in 9