Washington State Math Olympiad Hints and Solutions 2017 Grade 8 Probability and Statistics
Problem
1) Boitumelo can't remember his passcode. He remembers that it has five letters and that it begins and ends with a vowel. He also remembers that no letter is repeated in his code.
The picture below shows the keypad that he enters his code on (only the letters A through F). How many possibilities are there for his passcode?
2) Three six-sided dice are rolled. What is the probability that the sum of the 3 dice will be less than 6? Express you answer as a fraction in lowest terms.
3)
There are two bags. The first bag has 1 red marble, 2 blue marbles and 2 yellow marbles. The second bag has 4 red marbles, 1 blue marble, and 1 yellow marble. Josiah picks a bag at random. He then draws a marble at random from that bag. What is the probability that he draws a red marble?
Express your answer as a fraction in lowest terms.
Problem
4) What two numbers would you add to this list to make the median the same as the mode and to
make the mean 65?
60, 53, 71, 65, 61, 63, 57, 70
5) In how many unique ways can you arrange the letters of the word "ARRANGE"?
