Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2010 Grade 5 Probability & Statistics
Problem

1) Among the 78 fifth graders at Presley Elementary, 51 have at least one sister and 63 have at least one brother. How many have at least one sister and one brother?

2) A factor of 60 is chosen at random. What is the probability that this factor has factors of 2 and 5? Express your answer as a fraction.

3) The PTA is raising money with an auction and part of the auction is a raffle which allows you to draw from a jar of jelly beans. Each color bean is worth a different amount. There are 5 colors and they are in the following proportions: 7 red to 10 blue to 5 yellow to 5 green to 6 orange. There are 165 jelly beans in the jar. Red is worth $50, blue is worth $50, yellow is worth $100, green is worth $1 and orange is worth $20. If you are the first to draw, what is the probability that you will draw a bean worth at least $20? Express your answer as a fraction.

Problem

4) Toni's teacher gives a 20 point quiz every Friday. On her first five quizzes Toni has scores: 12, 10, 11, 20, and 12. What are the possible quiz scores for the next quiz that would keep the median the same but raise Toni's average? Quiz scores are whole numbers.

5) You are given the scrabble letter tiles that spell TRAVEL. How many three letter arrangements can you make with your tiles that have the pattern: vowel, consonant, vowel? The arrangements need not spell a real word though many will. (Note: since they are tiles you can use a letter only once.)