Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2011 Grade 5 Probability & Statistics
Problem
1) A bag contains some marbles of the same size. Twelve of them are red. The rest are all white. The probability of drawing a white marble is 2/3.
How many white marbles are in the bag?
2) Ted spends some afternoons throwing darts. The length of the board is 30 cm and the width is 20 cm as shown in the scale drawing. The outer grey band has a width of 5 cm on each side, the next white band has a width of 2 cm on each side and the inner white square has side length 2 cm. His darts always hit the board, but assume at random. What is the probability he will hit the inner light grey band? Express your answer as a reduced fraction (i.e. in lowest terms) or as a decimal rounded to the hundredths place.
3) A student got the following scores on her first five weekly math quizzes:
65, 82, 38, 86, and 74.
What is the least possible score she could get on the sixth quiz so that her median score would be 78?

Problem

4) Shooter's basketball team played in ten games.
The scores are charted as shown.
Which one is greater, the mean or the mode? By how much is it greater?

5) A gum ball machine is filled with an equal number of white, blue, yellow, green, and purple gum balls. You cannot control which color you get from the machine and the gum balls cost 25 cents each. How much would you have to spend to be sure of getting 3 gum balls of the same color?