Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2009 Grade 6 Probability and Statistics

Problem
1) The lowest number in a set of 5 numbers is 10. The range is 60 and the median is 50. What is the biggest the mean could be?

2) Katie and Jim play a game with 2 six sided number cubes numbered 1 through 6. When the number cubes are rolled, Katie gets a point if the sum of the two is even and Jim gets a point if the product is even. What is the likelihood that on one roll of both cubes neither Katie nor Jim get a point?

3) Bo, Darius, Kareena, Mary, and Paco all go with Mrs. Smart for math enrichment during math time. When they leave she lines them up by calling out their names, but she does this randomly. What's the probability that today Darius will be first and Paco will be last? Express your answer as a fraction.

4) Mr. Zee just can't play it straight. He's asked you to come over and help him paint his fence. He'll pay you based on the flip of 4 coins. If they all come up heads you get $100. For three heads you get $75, 2 heads $50 and for 1 head $25. No heads and you've just been a good neighbor. What's the likelihood you will earn at least $50 for this job?

5) Lelani is on a track team and wants to win in the 100 yard dash. Every day she runs as fast as she can. Her personal coach shows her the following table of her times over a 10 day period, but as you can see there isn't data for every day. How fast do you think Lelani will run on the 12th day?