Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2016 Grade 7 Probability and Statistics
Problem
Solution
1) If you flip 5 quarters, what is the probability that only one quarter will land face up?
(Express your answer as a fraction)
  1. Flipping 5 quarters at the same time, there are 25 possibilities = 32 possible outcomes.
  2. 5 of those are the probability of a single head (or tail for that matter), so the probability is 5⁄32
2) Jesse spun a game spinner and recorded his results in this table:
Outcome Frequency
 A 9
 B 6
 C 10
What is the probability of landing on B?
(Express your answer as a percentage.)
  1. There are a total of 9 + 6 + 10 = 25 occurrences of all 3 outcomes
  2. The probability of landing on B is 6/25 = 24%

3) There are five other players on Carter's kickball team. Kyle is the team captain and he picks the kicking order at random for each game. What is the probability that Carter will be the first to kick and Kyle will be the last?
(Express your answer as a fraction)
  1. There are 6 players on Carter's team
  2. The probability of Carter being first is 1⁄6
  3. After Carter is picked first there are only 5 players left, so the probability of Kyle being last is 1⁄5
  4. The probability of both things happening is:
        1⁄6 x 1⁄5 = 1⁄30

Problem
Solution
4) An estimate of the number of tagged foxes to the total number of foxes in a forest is 3:13. A forest ranger recorded 21-tagged foxes. How many foxes are in the forest if this observation is about 5% below expected of tagged foxes? Round to whole number. (Partial fox should not be included.)
  1. If 21 tagged foxes are 5% below the expected tagged foxes, then the expected tagged foxes are
    21/.95 = 22 foxes.
  2. Set up the following ratio:
        3 = 22
        13    x
  3. Solve for x:
        3x = 22x13

        x = 286 = 95.33 = 95 foxes total (rounded)
                3
5) Oren owns 6 shirts, 4 pairs of pants, and 3 pairs of shoes. If an outfit combination consists of one shirt, one pair of pants, and one pair of shoes, Oren's outfit combinations are reduced by how many when one of his shirts is thrown away?
  1. The total number of combinations Oren has is
    6x4x3 = 72
  2. When one of his shirts is thrown away the number of combinations is 5x4x3 = 60.
  3. This reduces his choices by 72 - 60 = 12