Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2013 Grade 6 Probability & Statistics
Problem
1) 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 what percent come from 1% milk?

2) Rina is making a necklace using 3 different colors of beads, Red, White and Blue, and a center stone. How many ways can she string 4 beads using all 3 colors of beads?

3) An 8 by 4 rectangular dart board has a triangle drawn inside of it that has two of its vertices at the midpoints of two sides of the rectangle and the third vertex at a vertex of the rectangle, see picture. If a dart is equally likely to hit any point of the rectangle, what is the probability the dart will land inside the triangle? Express your answer as a reduced fraction.

Problem
4) Jeron has been increasing his test average by 5 points with every test he takes. The tests are all out of 100 points. His first test score was a 60. He just got back his fifth test. What was his score?

5) To pass the time, Louisa and Maya are playing a game with a 12 sided die numbered 1 through 12 and a 20 sided die numbered 0 to 19. Louisa gets one point if the product of the two numbers is less than 60. Maya gets one point if the product is 60 or higher. What is the probability that Maya will get the point on the next roll? Express your answer as a reduced fraction.