Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2016 Grade 8 Probability and Statistics
Problem
Solution
1) A caterer is sorting silverware. There are 75 knives, 50 forks, and 75 spoons. Twenty of the forks and 30 of the spoons have red handles. If a piece of silverware is chosen at random, what is the probability that it will be a fork or have a red handle? Express as a simplified fraction. The probability of A or B is the probability of A + the probability of B.
  1. The probability of a red handle is 50/200 = 1⁄5
  2. The probability of a fork is also 50/200 = 1⁄5
  3. The combined probability = 1⁄5 + 1⁄5 = 2⁄5
2) A poll is taken and each person is asked two questions. The results are shown in the table. What is the probability that someone answered, "yes" to both questions? Express as a simplified fraction.
  1. The probability of a "yes" on the first question is 55/100 = .55
  2. The probability of a "yes" on the second question is 30/100 = .3
  3. The combined probability is
    .55 x .3 = .165 = 165/1000 = 33/200

3) An estimate of the number of tagged foxes to the total number of foxes in a forest is 3:13. A forest warden recorded 21 tagged foxes. About how many foxes are in the forest if this observation is low by about 5%? Round to the closest 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

Problem
Solution
4) If a baseball player has 18 hits in 50 at bats, what is the probability that he will get a hit in his next at bat? Express your answer as a percent. 18/50 = .36 = 36%

5) The circle graph below shows Art's Online total yearly sales by quarter. The total amount of sales for the year was $20 million. Find the sales for the 2nd quarter:
2nd quarter sales = $20,000,000 x .32 = 6,400,000