Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2010 Grade 7 Probability and Statistics
Problem
Hint
1) Mac is a Harry Potter fan and buys a box of Bertie Bott's Every Flavored Beans. He shakes out a handful. 6 are bogey flavored, 12 grass flavored, 2 chocolate, 9 earwax and 4 sardine flavored. He eats 3 of them. What is the probability that the 3rd one he eats is chocolate, assuming the first two were not chocolate?
  1. His handful was ____ beans.

  2. He eats 2 of them, so there are ___ left.

  3. There are still 2 chocolate beans left out of ___ so the probability is ______

2) Mr. Domani's class is playing multiplication bingo. Two dice are rolled and the numbers on the dice are multiplied together to get a product. Anna's board is pictured with the numbers she has crossed as products that have been rolled. What is the probability she will have a bingo with the next roll of the dice?
(Bingo means a row, column, or diagonal are all crossed out.)
  1. There are ___ numbers that will produce a bingo:

    These are _____________________

  2. Write out the dice combinations that result in these results (all of them) and then divide by the total number of dice combination possibilities = _____________

Problem
Hint
3) All 8th graders take a test and your teacher shows your class the results in a histogram and gives the exercise: represent the same data with a pie chart. Tina notices that one of the sections has an angle close to 90 degrees. What is the range of scores that goes with that section?
  1. An angle of 90 degrees in the pie chart corresponds to ___% of the scores.

  2. There were ____ total students.
  3. That percentage of the total is approximately ____ stidents, so the students that scored ____ to _____ were ____% of the students.

4) Tina's teacher gives a 20 point quiz every Friday. On her first five quizzes, Tina has scores of 15, 4, 16, 18, and 15. After the seventh quiz, her mean score is 15. What is the median?
  1. Re-arrange the scores in numeric order:

       
  2. There are 2 more scores to add. Try some candidate values for these 2 scores and determine what the median must be = _____
5) At the brand new middle school lockers open with PIN numbers instead of combination locks. PIN numbers consist of three one digit numbers and digits can repeat. This year all the 7th grade PIN numbers begin with 3, 4 or 5, but the other two can be any number from 0 up to 9. How big does the 7th grade class have to be to guarantee at least two students have the same PIN numbers?
  1. There are ____ ways to pick the first PIN digit.

  2. The other 2 digits are ____ digits each.

  3. The maximum number of PIN numbers is

    _____________, so the 7th grade class must be _____ to guarantee repetition of the PIN numbers.