Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2007 Grade 7 Probability and Statistics
Problem
1) 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?

2) A coin is weighted so that it comes up heads twice as often as tails. If it comes up heads 5 times in a row, what's the probability it will come up tails on the next toss?

3) The bar graph shows the test scores from a quiz for Mrs. Dalton's math class. Each question was worth 4 points and no partial credit was given. What was the class average to the nearest tenth of a point?

Problem
4) Roy is looking forward to making some good money once he's in high school. He does an informal survey of his older brother's friends. He puts the results of his survey in a table shown below. The local paper reports that the median wage for teenagers is $8.00/hour. Compute the median hourly wage for Roy's informal survey. Is the paper wrong or can you give another explanation for the difference?
5) Here's a game with one standard six sided die with the numbers 1 - 6. In at most three rolls of the die get as close to 10 as possible without going over. If you roll a 4 on the first roll, what's the probability you will go over 10 in the next two?