Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2006 Grade 6 Probability & Statistics
Problem
1) You are the manager of the girls' basketball team. The championship game is coming up, and the coach has asked you to determine from his statistics which of his top three players has the best record for free throws. Here is the statistical information that you have:
Joy made 21 out of her last 25 free throws.
Mary made 17 out of her last 20 free throws.
Nancy made 12 out of her last 15 free throws.
Tell the manager the order of his top 3 players: who is first, who is second, and who is third?

2) A set of 5 whole numbers all more than 0 but less than 10 has a mean of 5, a mode of 2, and a median less than the mean. What is the set of numbers?

3) Nora is considering inventing a language that consists of only three letter words. The words will all be made up of one vowel in the middle and 2 consonants so that they can be pronounced. She has decided to treat y as a vowel. How many different three letter "words" could be in her language?

Problem
4) Greg tosses 4 pennies in the air and they come up 3 heads and 1 tail. Express the probability of this happening as a reduced fraction.

5) A basketball team won 30 of the first 52 games it played. If this is a statistically accurate reflection of the team's abilities for the entire season, how many games are they likely to win of the next 18 games they play?