Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2011 Grade 6 Probability & Statistics
Problem
Solution
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? 1. Compute the area of the rectangle = 12 x 5 = 60 sq. cm.
2. Compute the area of the triangle = 2 x 3 / 2 = 3 sq. cm.
3. Divide the triangle area by the rectangle area =
    3/60 = 1/20
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? 		1. There are not 2 of any score yet, so if the mode and the median are the same, the median must be one of the 2 middle scores, 84 or 85.
2. Compute the mean using both of these numbers as the 7th score. One of them will match one of the two scores above.
    81 + 83 + 84 + 85 + 86 + 91 = 510
    Mean using 84: (510 + 84)/7 = 84.857
    Mean using 85: (510 + 85)/7 = 85
3. That score is 85
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? Wow! A plane with 12 seats per row!
1. There are 2 window seats per row and 4 aisle seats per row.
2. The number of seats that are neither is 12 - 6 = 6
3. Divide this by 12 to get the probability of not getting a window or aisle seat = 6/12 = 1/2

Problem
Solution
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? Since Lena is taking Theatre in the first session, the number of possibilities has to do with the selections for sessions 2,3, and 4.
Use G = gymnastics, D = drawing,
T = theatre and H = horseback riding.
The best way to do this is to list the possibilities. Here is a diagram of the 4 sessions, remembering that H is available only in sessions 2 and 3:
Session 1Session 2Session 3Session 4
TH or
G or D		H or
G or D
G or D
Here are the options:
Session 1Session 2Session 3Session 4
TH DG
THGD
TGHD
TDHG
There are 4 ways to schedule Lena's 4 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? 1. Chocolate chews are the least favorite, so make them 1 part
2. Then Fruit chews would be 3 parts and Gummy fish would be 5 parts, for a total of 9 equal parts of the chart.
3. Out of 360o multiply this by the fraction of the total parts that gummy fish have = (5/9) x 360 = 200o