Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2015 Grade 7 Probability and Statistics
Problem
Hint
1) Jen's warehouse receives a shipment of 700 refurbished toasters. She tests 40 of them at random for defects and finds 2 with power supply failure. If this sample is representative of the entire shipment, how many toasters should Jen expect to have power source failure? Multiply the number of toasters in the shipment by the fraction of them whose power supply failed in the test.

2) A set of five 2-digit whole numbers has a mean of 16, a mode of 13, and a median greater than the mean. What is the largest possible value of the largest number of the set?
  1. Compute the sum of the 5 numbers = _____

  2. There must be at least 2 13s (its the mode), so compute what the other 3 must add to and their average:
        Sum of the 3 numbers = ____

        Average of the 3 numbers ____

  3. For the median to be greater than the mean (16) it must be the lowest value possible to maximize the size of the last (largest) number. So, it must be _____.
  4. The next 2 numbers must be higher than this number to keep it the median (middle number), so their total must be
        ______ and their average must be
        ______
  5. Call the last 2 numbers X and Y. Y is the one we are trying to maximize)
  6. Here's where you have to play around with candidate numbers and see what fits, making sure you don't violate any of the problem specifications.
        The largest number is _____

Problem
Solution
3) You have a bag containing 5 red candies, 7 blue candies, 8 green candies, and 12 yellow candies. If you pull candies from the bag at random, what is the minimum number you would have to take to ensure getting 3 of at least one color? To insure getting 3 of at least one color, you have to assume that you make the worst picks, which is to pick one of each color until you must pick a third of some color.

So, the minimum number to insure getting 3 of at least one color is _____
4) A six-sided die is weighted so it rolls 6 five times as often as any other number. If it rolls 6 five times in a row, what is the probability it will roll 6 on the sixth roll?
  1. The fact that it has rolled 6 5 times in a row is irrelevant. That is in the past.
  2. There are 5 other numbers and the 6 rolls 5 times any other number, so the possible rolls are:
        _________________________,
    making the probability that it will roll a 6 ____ %

5) There are 5 little league baseball teams in your county. There are 4 teams in a neighboring county. Each team will play three games against each of the other teams within their county and two games against each of the teams in the neighboring county. How many total games will be played by the end of the season? 		Note: When selecting 2 teams out of a league to play each other, that is a combination.
When selecting 2 teams that are not in the same league, that is a permutation
  1. Games in your county:
        ___________
  2. Games with neighboring county teams:
        _____________
  3. Games the neighboring county plays with themselves = ___________
  4. The total number of games played is ___________ games