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 ____ numbers to pick for the first number of the combination.

  2. The second number cannot duplicate the first so there are ____ numbers available for it.

  3. The last number cannot dupicate the second but it can duplicate the first, so there are _____ numbers available for it.
  4. Total combinations = ________
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 ______

Problem
Solution

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. Sum up the heights of each bar to get the total number of students. This is
    _______


  2. Multiply the number of students in each bar by the bar's score and add:


    The total of the scores is _____________

  3. Divide by the total number of students to get the class average =


    ________________
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 =


    _________ friends
  2. The median is the middle one
    (counting from either end) = $______
    The reason for the difference between Roy's survey and the paper's is



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 ____, so this is the probability of rolling a sum of ____ or higher with 2 dice.
  2. Examine this table of the sum of 2 dice.


    The probability is ______