Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2017 Grade 5 Probability & Statistics
Problem
Solution
1) Two fair six-sided dice are rolled. What is the probability that the product is even? (express your answer as a fraction in lowest terms) 1. The total number of combinations of two dice is 6 x 6 = 36.
2. What proportion of the products are even? 27/36
3. Express this fraction in lowest terms = 3/4

2) How many ways can you arrange the letters in the word "MATH"?		 This is a permutations problem.
1. How many ways to pick the first letter: 4.
2. How many ways are there to pick the second letter? 3
3. After those picks how many ways can you pick the third letter? 2.
4. How many ways to pick the last letter? 1
5. Multiply these together to get the total number of ways of arranging the letters in "MATH". = 4 x 3 x 2 x 1 = 24
3) There are 5 red balls, 2 yellow balls, and 1 orange ball in a bag. You will select a ball without looking and then put it back. If you do this 60 times, how many times would you expect to pick a yellow ball? 1. What is the total number of balls? 8
2. What is the fraction of the total that are yellow? 2/8 = 1/4
3. Multiply this fraction times the number of picks = 60 x 1/4 = 15

Problem
Solution

4) What number would you add to this list to make the median the same as the mode?
    75, 63 75, 20, 15, 70, 63, 21 		1. Rearrange the numbers into numerical order:
    15, 20, 21, 63, 63, 70, 75, 75
2. The median of this set is 63.
3. Since there are 2 63s and 2 75s, in order to have a single mode you must add a 63.

5) The mean of 4 numbers is 16. When the smallest number is removed, the mean of the remaining 3 numbers is 17. What number was removed?		 This is actually an algebra problem.
Call the smallest number N
Call the sum of the 3 larger numbers N3
1. Write an equation for "the mean of 4 numbers is 16" using the above variables: (N + N3)/4 = 16
2. Write an equation for "the mean of the remaining 3 numbers is 17" using the above variables = (N3)/3 = 17
3. Solve the second equation for N3 = 51
4. Using this value for N3,put it in the first equation and solve:
    (N + 51)/4 = 16
    N + 51 = 64
    N = 64 - 51 = 13