Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2014 Grade 7 Probability and Statistics
Problem
Hint
1) Miguel entered a contest offering prizes to the top 3 finishers. The probability of winning 1st place is 12%, the probability of winning 2nd place is 18%, and the probability of winning 3rd place is 20%. What is the probability that Miguel will not win any prize? Express your answer to the nearest percent. Just add the percentages.

2) Douglas MS participated in a contest with the results shown. If five teams participated, what is their highest score? (Try and create a data set that works.)
  1. OK, we have a data set of ___ numbers whose median is ___, whose mean is ___ and whose range is ___.
  2. Since there are an odd number of members then the middle score is ___
  3. The mean of the other 4 scores is


      mean = _____
  4. Based on whether this mean of those 4 scores is greater or lower than the median, put together candidate values in sets of 5, making sure you keep the range 8. If the mean of those 4 numbers is less than the median, then having a number higher than the median will raise the lowest number and raise the mean.


  5. Continue to play around with values until all conditions in the problem statement are met.
  6. The highest score is _____
3) An airplane is built to be able to fly on one engine. If the plane's two engines operate independently, and each has a 1% chance of failing in any flight, what is the chance a plane would fail to complete a flight? Express your answer as a percent. You can't do arithmetic with percentages until you convert them into either fractions or decimals. We'll use fractions. Convert the probabilities to fractions and multiply the 2 probabilities together:


    Probability = _____ %

Problem
Hint
4) When rolling a single six sided die three times, how much more likely are you to roll all three different numbers compared to all three the same number? Express your answer as a ratio.
  1. All 3 are the same number:
        The first roll establishes what number will be replicated
        Probability of the second roll matching the first:

          _____
        Probability of the third roll matching the first:

          _____
        total = _______
  2. All are different.
    The first roll establishes one number,
    the second has 5 remaining numbers and
    the 3rd 4 remaining numbers:
    Use these values to compute this probability:


          = ______
  3. Divide the first probability by the second:


        = ______
5) There are 25 students in Mr. B.'s class. Tori is one of the students who has a $2.00 weekly allowance. Which average, mean or median, should she report to her parents to encourage them to give her a higher allowance? Write your choice and its value.
  1. Compute the mean:


        = _____
  2. Compute the median.

    = _____
  3. The highest one is _____