Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2012 Grade 5 Probability & Statistics
Problem
Solution
1) In the Monopoly board game, a player tosses two six sided dice and adds the two resulting numbers to determine the number of spaces to move the playing piece. Albert wants to play Monopoly with his friends but can't find the dice. He finds a 12 sided die with the numbers 1 through 12 on it to replace the two regular 6 sided dice. What is the ratio of the probability of rolling a 7 with the two 6 sided dice to the probability of rolling a 7 with the 12 sided die? Express your answer in the format "whole number : whole number". 1. How many ways can you roll a 7 with 2 dice? 6 ways:
    (6,1) (5,2) (4,3) (3,4) (2,5) and (1,6)
2. With a 12-sided die how many ways can you roll a 7 with only 1 of these funny dice? 1
    (there is only one 7 on a 12-sided die.)
3. To get the probability of each of these occurrences you divide the number of ways (above) by the number of possibilities for each.
    Probability with 2 dice = 6/36 = 1/6.
  Probability with 1 12-sided die = 1/12.
4. Divide the first probability by the second to get the ratio of these 2 probabilities = (1/6)/(1/12)= 2 : 1.
2) The average (mean) of 3 numbers is 21. If the smallest number is removed, the average of the remaining 2 numbers is 27. What is the value of the number that was removed? 1. The sum of the 3 numbers is 63.
2. The sum of the 2 remaining numbers is 54.
3. Subtract #2 from #1 to get the 3rd number = 9
3) On Saturday Megan likes to go to Sandwich Heaven.
Megan chooses the bread, filling, and topping for her sandwich.
She can choose between wheat, rye, or white bread.
She can have chicken salad, turkey, or ham for the filling.
She can also have lettuce, tomato, or sprouts on top.
How many different sandwiches can Megan choose from if she always chooses a filling and a topping with the bread?		 1. How many bread selections are there? 3
2. How many filling selections are there? 3
3. How many topping selections are there? 3
4. Multiply these three number of selections =
    3 x 3 x 3 = 27.

Problem
Solution
4) A group of parents were discussing baby statistics. One person said she had heard a report that for every 100 babies born, there were 6 more boys than girls. Based on this, if a baby is randomly selected from the hospital nursery, what is the probability the baby is a girl? 1. If, out of a hundred babies, there are 6 more boys than girls, how many girls were there? 47
    (53 boys and 47 girls makes 6 more boys than girls)
2. Divide this by the total number of babies to get the girl probability = 47 / 100 = 47%.
5) Sol takes a survey of the entire 5th grade class on the kinds of pizza they would enjoy eating and presents his findings in the bar graph shown. He only offers three choices: cheese, pepperoni and Hawaiian. There are 90 students in the 5th grade class. At most how many students like only cheese pizza? (think of what the data might look like in a Venn Diagram). 1. Suppose that everyone who likes Hawaiian pizza also likes pepperoni.
  This would be the case for the maximum number of cheese-liking-only students.
2. Then that number of students = 60.
3. The remainder of the 90 students like cheese only.
    That number is 90 - 60 = 30 students.

Here is the Venn diagram of that: