Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2011 Grade 6 Probability & Statistics
Problem
1) A rectangle is 5 cm long and 12 cm wide. A triangle with a 2 cm base and 3 cm height is drawn inside the rectangle. What is the probability that a random point inside the rectangle is also inside the triangle?

2) Ava's teacher tells her that the median and mode are equal for her seven test scores including the one she hasn't passed back yet. Ava knows her first six scores: 81, 83, 84, 85, 86, 91. The teacher tells her that the mean of all seven test scores is also one of the scores she already knows. What is the seventh test score?

3) Rudi is flying to Ireland to meet his aunt for the first time. The coach seats in his plane are arranged in 25 rows with two aisles splitting each row of seats so that three seats are on the left side, six are in the middle and three are on the right side. Each row has a window seat on the left and on the right side of the plane. If seats are assigned randomly, what is the probability that Rudi won't get a window or an aisle seat?

Problem
4) Lena is signing up for classes at her summer camp. She wants to take gymnastics, horseback riding, drawing, and theatre. Gymnastics and drawing are offered all four sessions. Horseback riding is offered session 2 and 3. Theatre is offered session 1 and 4. She is going to take each class once and take one class each session. If she wants to take theatre the first session, in how many ways can she schedule all four classes?

5) Mr. Sweets concession stand is selling small bags of chocolate chews , fruit suckers, and gummy fish this season. Fruit suckers are selling 3 times as fast as the chocolate chews and the gummy fish are selling five times as fast as the chocolate chews. His one worker makes a pie chart to prove to him why he should order more gummy fish than the others. What angle should the gummy fish piece have?