Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2015 Grade 5 Probability & Statistics
Problem
Solution
1) Your parents give you $1.25 for doing one chore and they double that amount for every additional chore. If you earn $8.75, how many chores did you do? 1. The amount you earn for the second and subsequent chores is $2.50.
2. Subtract the first chore pay from the total = $7.50.
3. Divide this amount by the amount for the second chore =
    $7.50/$2.50 = 5 chores.
4. Add the first chore to get the answer = 6 chores
2) What is the probability of rolling a sum of 9 with 2 six-sided dice?
(Express your answer as a fraction in lowest terms )
Method 1: Fill out the table, find the number of ways to get a sum of 9 and then divide by the total number of possibilities.

There are 4 ways to get a 9 and 36 possibilities for a probability of 1/9 		Method 2:
With 2 6-sided dice, how many ways can you make a sum of 9?
(4,5) (5,4) (6,3) (3,6) = 4 ways. How many total possibilities are there? 36.
Divide these and the probability is 1/9

Problem
Solution
3) The average of 4 numbers is 18. If the largest number is removed, the average of the remaining 3 numbers is 15. What is the value of the number that was removed? This is actually an algebra problem.
Let N3 be the sum of 3 of the numbers.
N is the number to be removed. Then
    (N3 + N)/4 = 18
    N3/3 = 15 (the average of the 3 numbers), so
    N3 = 45
Substitute this value in the first equation and solve for N
    (45 + N)/4 = 18
    45 + N = 72
    N = 72 - 45 = 27
4) Riona has a clothes drawer containing socks. She has 13 white socks, 12 red socks, 7 blue socks, and 4 green socks. If she takes one sock out at random, what is the probability of drawing a red sock? (Express your answer as a fraction in lowest terms ) 1. What is the total number of socks in Riona's drawer? =
    36
2. Divide the number of red socks by this number to get the probability of drawing a red sock = 12/36 = 1/3

5) Given the blanks in the following list of whole numbers, such that the mean and median will be 17 and there will only be one mode . What is the mode?

      3, __, 11, __, 16, __, 20, 23, 28, 32 		1. There are 10 numbers (including the blanks) in this list.
2. For the median to be 17, then the two middle numbers must average to 17.
3. One of those numbers is 16, so there must be an 18 to made the median 17. (16 + 18)/2 = 17
      3, ___, 11, ___, 16, 18, 20, 23, 28, 32
4. The sum of the now 8 given numbers is 151.
5. To average to 17, this sum of 10 numbers must add to 170
6. Subtract this from the sum of the given numbers =
    (170 - 151) = 19
    This is the sum of those 2 blank numbers.
    (A + B) = 19
Since this is a list of whole numbers, they cannot be the same number.
7. So, one of them must be the same as one of the existing numbers in the list to make a single number a mode.
8. The only numbers that qualify are 8 and 11, making the mode 11
    The final list is:
      3, 8, 11, 11, 16, 18, 20, 23, 28, 32