Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2007 Grade 6 Probability & Statistics
Problem
Hint
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. Take the average of the 2 semester GPAs = _____

2) 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
 1. Since there are two 23s in this list, the number of 9s must be ___ to make it the mode.
2. Since there are 10 numbers in this list, the median must be the average of the middle 2 numbers.
3. What number, averaged with 13 is 15? _____
4. The completed list is: ____________________

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?		 1. Add the probabilities of orange and lemon chews = ____
2. Subtract this from 1 = _____. This is the probability of a strawberry or a cherry chew.
3. Using this, compute the total number of chews = _____

Problem
Hint
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? Consider the figure to the right. Bill is at E and straight ahead is toward B. Left takes him to D and right to F. He can't go to H directly because that is backward. This should help you visualize the moves.
1. So, at each of 4 moves, he has 3 choices, left, right or straight ahead, so the number of possible combinations is ___
2. Work out the move combinations that get him back to his start (point E in the diagram).
    Using L = left, R = right and S = straight ahead,




    There are ___ of those.
3. The probability of ending up at the start is _____

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? 		1. There are ____ possible numbers.
2. How many ways to get the first number? ___
3. How many ways to get the second number if it can't match the first? ____
4. How many ways to get the third number if it can match the first number but not the second = ___
5. Multiply these possibilities together = _____ combinations.