Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2013 Grade 5 Probability & Statistics
Problem
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 cake cupcake?

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?

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?

Problem
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?

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?