Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2008 Grade 8 Probability and Statistics
Problem
1) There are two coins in a bag, one that has heads on both sides and one that is weighted so that heads comes up twice as often as tails. What are the odds of randomly selecting a coin out of the bag, flipping it, and having it land on tails?

2) A data set consists of seven different positive whole numbers. The mean of the data is 69. What is the largest the median of the data could be?

3) Joan and David invent a probability game for a homework project that has players flip a fair coin and roll a fair 6 sided number cube with the number 1 - 6 on it and move pieces on a board with 50 spaces on it. David moves ahead on the game board as many spaces as the number that comes up on the number cube when the coin lands on a heads. Joan moves ahead three spaces each time the coin lands on a tail no matter what number comes up on the cube. After two roll and flip combinations who is more likely to have moved at least 6 spaces and with what probability?

Problem
4) Most Washington license plates consist of a set of three numbers followed by a set of three letters. A witness sees a suspicious car and reports it to the police. He says the first two numbers were 4 and 6 but he missed the third and the first letter was C. How many possible license plates does that describe?

5) The data and the scatter plot of the data show the relationship between foot length of an adult male and his height. A footprint of a burglar is found outside the window and has a length of 30 cm. John is asked to predict a height for the burglar. He draws a line of best fit and finds it has a slope of 3.7 and passes through the data point (26, 173). What is John's prediction for the height of the burglar?