Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2006 Grade 7 Probability and Statistics
Problem
Solution
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?
  1. If the mode is 2 then the other 3 numbers must average ______

  2. If the median is less than the mean (5) then the median must be ___ or ____
  3. Examine the 2 possibilities for the median to get the whole set =



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

 The best way of solving a problem like this is just listing the possibilities.
Using H for heads and T for tails, make a table of possibilities.
I'll do the first row for you:
    H   H   H   H
















    The probability is _____

Problem
Solution
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.
  1. Convert .75 to a fraction = __________


  2. The product of the 2 probabilities is ______
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? Note: Ignore the data about pizza and tape.
  1. Toilet paper: 69% of 36 = ____ students

  2. Zippers: 42% of 36 = ____ students

  3. Compute the sum of these 2 number of students. Any over 36 will be the overlap = _____ students.
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. If you let your little brother randomly pick one coin from this handful, what's the chance he ends up with a Canadian penny?
  1. The probability of getting a Canadian penny in change is _____

  2. Compute the number of pennies this is = _____ pennies.

  3. There are a total of ____ coins so the the probability is:

    ______________