Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2008 Grade 5 Probability & Statistics

Problem
Solution
1) A dart hits the dartboard shown at random. Find the probability of the dart landing in the shaded region.
  1. Dark area = (6 x 1)/2 = 3
  2. Total area = 9 x 1 = 9
  3. Ratio (probability of hitting the dark area) = 3/9 = 1/3
2) Jazmin has a coin and Sue a 6 sided number cube labeled 1 through 6. They have decided to play a game. What is the probability that Jazmin will flip a head and Sue will roll an even number? What is the probability of a coin being heads? 1/2
What is the probability of a 6-sided die
    coming up an even number? 3/6 = 1/2
Multiply the two:1/2 x 1/2 = 1/4 or 25%

Problem
Solution
3) Four friends, Amber, Becky, Callie, and Darcy went to a party. If Callie was the third to arrive, how many different orders could the other three friends have arrived in? The number of permutations of 3 things is 3 x 2 x 1 = 6
4) After three tests Max has a test average of 83. He is nervous for the fourth test and wants to keep an average of at least 80. What is the lowest score he can get on the fourth test if each test is worth 100 points? The equation for the mean:
    (83 + 83 + 83 + X)/4 = 80
    (249 + X)/4 = 80
    249 + X = 320
    X = 320 - 249 = 71
5) A class of 21 children goes to the gym to measure its length in paces. The bar graph shows the distribution for the number of paces it took to traverse the gym lengthwise. All numbers are whole numbers. From the graph which bar contains the median number of paces?
After you cross off the first 4 highest and lowest you should notice that there are more in the 46-50 pace column than in the 41-45 pace column, making the median number of paces fall in the 46-50 pace length bar.