Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2007 Grade 6 Probability & Statistics
Problem
1) Onita is pretty sure her semester GPA will be 3.8 for the 6 credits she's taking. Her previous cumulative GPA was 3.5 for the 6 credits she already had from the previous semester. What will be her new cumulative GPA? Round to the nearest hundredth.

4) Fill in the blanks in the list of numbers such that the only mode for the list will be 9 and the median will be 15.
4, 9, ___, ___, 13, ___, 17, 23, 23, 28

3) Joe's dad tells Joe he can have the bag of fruit chews he's holding if he can solve this riddle. There are four flavors: strawberry, orange, lemon, and cherry. There are 5 strawberry chews. The probability of getting orange is 1/7. The probability of getting a lemon is 2/7. What is the fewest number of cherry chews that could be in the bag?

Problem
4) Mr. Bill arrives at an intersection in the middle of a city and realizes he is totally lost. The streets form a grid with each block a square. They all look the same to him and the fog isn't helping any. At each intersection he has a choice of three directions to go in: left, right or straight ahead. If he chooses a direction completely randomly at each intersection what is the probability that after 4 more moves, he is right back where he started?

5) A company puts out dial combination locks that open by turning a dial clockwise to get to the first number, counterclockwise to get to the second number and clockwise to get to the last number. If the numbers on the dial are 0 through 5 and neither the first two nor the last two numbers can be the same, how many different combinations are there?