Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2012 Grade 7 Probability and Statistics
Problem
1) Robin owns 5 shirts, 3 pairs of pants and 2 pairs of shoes. Robin hates wearing the same outfit twice. Robin wears one shirt, one pair of pants and one pair of shoes each day. How many more outfit options will Robin have if he adds one more pair of pants to his collection?

2) An octahedral die has the numbers 1 - 8 on its sides and has an equal chance of landing on any of its sides. What is the probability of rolling the same number three times in a row?

3) It's jelly bean contest time. To change the contest a little, the librarian has students guess how many purple jelly beans are in the jar. Tilly applies a little statistics. She counts 36 jelly beans pressed up against one side of the jar and then counts 8 purple out of the 36. She also estimates that there are 520 total jelly beans in the jar. Based on these estimates and thinking that the jelly beans are pretty well mixed, what is a good estimate for the total number of purple jelly beans in the jar?

Problem
4) Jerri is trying to perfect her archery skills and has created a small 8 inch by 8 inch square target with an even smaller triangular region inside as shown. Initially she hits anywhere in the target at random when she hits it at all. What is the probability that she hits the triangle when she hits the square target?
5) Sweet Raisins sells 1.5oz boxes of raisins. Not all the boxes have the same number of raisins. In a quality control check 25 boxes were randomly selected and checked for weight and number of raisins. The graph displays the data for the number of raisins. What is the positive difference between the mean and the median number of raisins for these boxes?