Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2009 Grade 5 Probability and Statistics
Problem
Solution
1) Katie and Jim play a game with 2 six sided number cubes numbered 1 through 6 (dice). When the dice are rolled, Katie gets a point if the sum of the two is even and Jim gets a point if the product is even. What is the likelihood that on one roll of both cubes both Katie and Jim get a point?
  1. The probability of Katie rolling an even sum of 2 dice is 1/2
  2. The products of two dice:
  3. There are 27 even products = 27/36 = 3/4
  4. The probability of them both getting a point =
        1/2 x 3/4 = 3/8.
2) Randy opens up a bag of jelly beans after mixing them up. He pours out 10 and counts 4 red ones in the bunch. He wants to practice his knowledge of statistics and has his brother count all the jelly beans in the bag in another room. There are 160 according to his brother. Based on Randy's sample, about how many red jelly beans should be in the bag? 1. Find the probability of getting a red jelly bean
    using Randy's data: = 40%
2. Apply that same probability to the entire 160 bean bag: =
    64 jelly beans.

Problem
Solution
3) The students in Mr. Beloshi's class are working in groups to draw a life size average fifth grader for their class of 25 students. Group A has gathered data about all the fifth graders in their class. Heights to the nearest inch are shown in the bar graph.

To the nearest inch, what is the mean height and what is the median height? 		1. The average is 1372/25 = 54.88.
    Rounded = 55 inches
2. The median height is 54 inches.
4) Mr. Zee just can't play it straight. He's asked you to come over and help him paint his fence. He'll pay you based on the flip of 3 coins. If they all come up heads you get $100. If two heads, then $75, if one head $50 and no heads $25. What's the likelihood you will earn more than $50 for this job?

 Here is a table of all possibilities:
Coin 1Coin 2Coin 3     $    
headheadhead $100
headheadtail $75
headtailhead $75
headtailtail $50
tailheadhead $75
tailheadtail $50
tailtailhead $50
tailtailtail $25
There are 4 combinations producing a pay over $50
so the probability = 4/8 = 1/2
5) If the pattern of the first six letters in CIRCUSCIRCUS . . . continues, then the pattern's 500th letter is? Divide 500 by 6 = 83 remainder 2. The 500th letter is the second letter, I.