Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2013 Grade 5 Probability & Statistics
Problem
Solution
1) In a box of 12 assorted cupcakes, 1/3 are chocolate, 1/2 are poppyseed, and the rest are red velvet cake. 1/4 have chocolate frosting, 1/2 have cream cheese frosting, and 1/4 have vanilla frosting. If you pick cream cheese frosting you have an equal chance of it being a chocolate, a poppyseed, or a red velvet cupcake. If you don't pick cream cheese frosting, what is the likelihood that you will get a chocolate cupcake? 1. The fact that picking a pink cream cheese frosting gives you an equal chance of it being a chocolate, a poppyseed or a red velvet cup cake means those cupcakes occur in the same numbers with pink cream cheese frosting. 2. In a box of 12 assorted cupcakes if 1/3 are chocolate that makes 4 chocolate cupcakes.
3. If 1/2 are poppyseed, that makes 6 poppyseed cupcakes.
4. The rest being red velvet means that 2 cupcakes are red velvet.
5. If 1/2 of the cupcakes have cream cheese frosting then 6 cupcakes don't have cream cheese frosting.
6. If there is an equal probability of a cupcake having a cream cheese frosting, then there must be 2 of each cupcake flavor having that frosting.
7. Then 6 cupcakes must have another frosting.
8. Subtract 2 from each cupcake flavor leaves
    2 chocolate, 4 poppyseed and 0 red velvet cupcakes.
9. The probability of getting a chocolate cupcake that doesn't have cream cheese frosting 2/(4+2) = 2/6 = 1/3

2) In Mr. Zeda's class all the quizzes are out of 10 points. Julio current list of scores is 8, 4, 9, 8, 6. He takes the next one and his average doesn't change. What did he score?		 1. Julio's next score must be the mean for the average (mean) not to change.
2. Compute the mean of Julio's scores =
    8 + 4 + 9 + 8 + 6 = 35/5 = 7 points

Problem
Solution
3) Trina has to do an environmental art project. She chooses to do one with the bottle caps from gallon milk containers and asks her friends to help collect them. She gets a total of 1000 bottle caps and they come in red - whole milk, blue - 2%, yellow and green - 1%, and white - skim. She mixes them all up in a box and pulls out the first handful of 20 to begin her project. There are 3 red, 5 blue, 3 yellow, 4 green, and the rest are white. If this handful is a good representation of all 1000 bottle caps, about how many come from 1% milk? 1. Both yellow and green are 1% milk caps.
2. Yellow and green make up 7/20% of her handful of 20 caps.
3. That percentage of 1000 is 350 caps.

4) Rina is making a necklace using 4 different colors of beads and a center stone. How many different ways can she string 4 beads using all 4 colors?		 This is a permutations problem.
1. With 4 colors there are 4 ways to pick the first color.
2. Then, there are 3 ways to pick the second color.
3. Then, there are 2 ways to pick the third color.
4. There is 1 way to pick the last (4th) color.
5. Multiply these to get the different ways =
    4 x 3 x 2 x 1 = 24 ways.
5) At the beginning of each school year, Joey and Mateo's mom marks off their heights on the kitchen wall. She plots the growth gaps on a growth chart to see the growing patterns of her two boys. Based on the chart, who grew more in total and by how much from 1st through 7th grade?
 1. Add up Joey's growth from the 1st thru 7th grades =
    3 + 2 + 3 + 2 + 2.6 + 3.8 + 3.4 = 19.8 total inches.
2. Add up Mateo's growth from the 1st thru 7th grades = ____ total inches.
    2 + 2.4 + 1.8 + 1.8 + 2.4 + 3.4 + 5 = 18.8 inches
3. Joey grew more by 1.0 inch.
Any answer from .8 to 1.2 inches is acceptable.