Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2008 Grade 5 Probability & Statistics
Problem
Hint
1) A dart hits the dartboard shown at random. Find the probability of the dart landing in the shaded region.
This is actually a geometry problem. Find the ratio of the dark area to the total area (not the white area):
  1. Dark area = __________
  2. Total area = _________
  3. Ratio (probability of hitting the dark area) = _______
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? ____
What is the probability of a 6-sided die coming up an even number? ___
Multiply the two: ______
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 fact that Callie was the third to arrive makes this a 3-person permutation problem. The fact that Callie arrived 3rd is irrevelant. How many ways can you order 3 things or persons ? _____

Problem
Hint
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? This is actually an algebra problem. You can use 83 for the first 3 tests and X for the 4th to average to 80.
Write the equation for this and solve:

X: _______
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?
 The median is the one in the middle, not the average. The key is to use the 'cross off' method: cross off the highest then the lowest, next highest, next lowest and continue until only one is left. On the graph, put a horizontal line through the highest, lowest and continue until only one is left. The last one crossed out is in the ____ range of paces.