Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2012 Grade 5 Probability & Statistics
Problem

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".

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?

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?

Problem

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?

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).