Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2007 Grade 7 Probability and Statistics
Problem
Solution
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?
  1. There are 6 numbers to pick for the first number of the combination
  2. The second number cannot duplicate the first so there are 5 numbers available for it.
  3. The last number cannot dupicate the second but it can duplicate the first, so there are 5 numbers available for it.
  4. Total combinations = 6x5x5 = 150
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? Probability is NOT dependent on what has happened in the past!
The probability of tails is 1⁄3

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?
  1. The number of students is
    3 + 6 + 8 + 5 + 1 = 23
  2. The total scores are
    24x3 + 28x6 + 32x8 + 36x5 + 40x1 = 716
  3. The class average was 716/23 = 31.1

Problem
Solution
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?
  1. Total up the frequencies to get the number of friends he surveyed =
    1+3+2+2+3+3+2+2+1+1 = 21
  2. The median is the 11th (counting from either end) = $9
    The difference between Roy's survey and the paper's is sample size. The paper probably had more data.
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?
  1. Rolling a 4 on the first roll leaves 6, so this is the probability of rolling a sum of 7 or higher with 2 dice.
  2. Examine the table to the right. The probability is 21/36 =
    7⁄12