Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2012 Grade 6 Probability & Statistics
Problem
1) Mercedes is looking at the calendar for the month of May 2012 and sees May 5th is a Saturday. If she draws a box around four dates that all touch at a corner, what is the probability the box contains two dates that are multiples of 6? (May has 31 days.)

2) Lucy is playing a cup game with her brother. She has 10 cups turned upside down in front of her. She has hidden 5 pieces of candy, one under each of 5 cups. To get all the candy, her brother has to uncover three pieces of candy in the first three tries. What is the probability that he will win all the candy?

3) LaMarcus does a survey of 57 students about the pets they own. There are 870 students in his school. If the survey is an accurate reflection of pet ownership at his school, what percentage of students are cat owners?

Problem
4) Tad needs to maintain an 85 or higher average in math class for his parents to let him play on two sports teams. His current average based on four test scores is 94. He doesn't have much time to study for the next test. What is the lowest he can score on the next test to maintain an 85 or above average?

5) Doreen likes to play Words with Friends, a version of scrabble, on her phone. She has a Z, two vowels and two consonants left, and the letters are all different. Her strategy in this round is to try combinations using her Z for 10 points, a vowel, and one other of her letters in that order someplace on the board and see if they work. How many different options does she have for the three letter combinations without considering where they'll go on the board?