Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2006 Grade 7 Probability and Statistics
Problem
1) A set of 5 whole numbers all more than 0 but less than 10 has a mean of 5, a mode of 2, and a median less than the mean. What is the set of numbers?

2) Greg tosses 4 pennies in the air and they come up 3 heads and 1 tail. Express the probability as a reduced fraction.

3) In a video game, each fireball launched has a 75% chance of hitting a target. What is the probability that exactly 2 fireballs will hit the target when 2 fireballs are launched? Express your answer as a reduced fraction or as a decimal to the hundredths place.

Problem
4) A group of 36 students are interviewed about some items they would not want to do without. These were the results rounded to the nearest whole number percent. What is the smallest number of students that could have selected toilet paper and zippers as items they don't want to do without?
5) A store in Vancouver, Washington finds to its disgust that they have managed to collect many Canadian pennies. They decide to hand them back to the public since that's where they came from in the first place. To make it less obvious they divide them up between tills so that the mix of Canadian to American pennies is about 1 to 3. You get a small handful of change from this store consisting of 2 quarters, 1 nickel, 3 dimes and 8 pennies (they ran out of quarters and nickels). If you let your little brother randomly pick one coin from this handful, what's the chance he ends up with a Canadian penny?