Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2009 Grade 6 Probability and Statistics
Problem
Hint
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? 1. Here are the numbers:
    10 ___ ___ ___ ___
2. If the range is 60, the last number must be ____.
3. Place the median number in the above list.
4. Fill in the other two numbers, preserving both the maximum and the median with the highest numbers that do this:

5. Compute the mean of these numbers = _____
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? Here are the sums and products of 2 dice:
SUMS
PRODUCTS
Examine these tables and find the probability that Katie's roll will be odd and Jim's roll will produce an odd product = _____

Problem
Hint
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. 1. There are ____ students total.
2. The probability that Darius will be the first is ____
3. After you choose the first, what is the probability that Paco will be the last? ____
4. Multiply these two probabilities together to get the probability that both will happen = _____

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?		 1. With 4 coins, there are _____ possible combinations.
2. The only combinations where you don't get $50 are when all 4 coins are tails which is _____ combination and when only one hsi a head, which can occur in _____ ways.
3. Total these ways and subtract them from the total to get the number of ways you can get $50 or more = _____.

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?
 1. Over a 9 day period Lelani dropped ____ seconds from her 100 yard dash time.
2. Compute the rate of improvement in seconds/day = _____
3. Apply that to day 12 based on her day 10 time.
Day 12 time = ______