Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2011 Grade 8 Probability and Statistics
Problem
Solution
1) A new Hogwarts student needs to buy a wand. At the wand shop there are 270 wands available. There are 4 wands that are perfectly suited for her. There are 36 wands that would work ok but are not optimal. What is the probability that she will pick either a perfectly suited wand or an ok wand within the first two tries if she selects at random without replacement? You may give your answer as a numerical expression or as a decimal to the nearest hundredth. The probability of getting either a perfect or OK wand is 1 - the combined probability of NOT getting a perfect or OK wand on either try, so:
  1. Probability of a miss on the first try =


  2. Probability of a miss on the second try, assuming you missed on the first try:



  3. Probability of getting a perfect or OK wand =
    1 - the product of these miss probabilities =


2) Scientists are monitoring a long lived parrot species in a jungle. One year they are able to find and tag 50 parrots. The next year they find 50 parrots again but only 15 of those parrots are tagged. Based only on this data, what is a good estimate for the population of parrots in this jungle?
  1. Those 50 tagged parrots were _______ of the total population.
  2. Divide these 50 parrots by the fraction found in the previous monitoring to get an estimate of the total parrot population:



    = _____ parrots.

Problem
Solution

3) A gumball machine holds 96 gumballs. They come in yellow, red, blue, and white. There are twice as many yellow as red gumballs, twice as many blue as yellow gumballs, and as many white as there are blue and red together. What is the probability of randomly getting a white gumball from the machine? Express your answer as a simplified fraction.
  1. The fewest number of gumballs is red.
    Assume there is 1 red gumball
  2. Yellow = ____
  3. Blue = ____
  4. White = ____
  5. Total = ____
  6. There are ____ whites so the probability is _________
Note: You don't need the total number of gumballs
4) A palindromic number is one which is the same read backwards and forwards. For example, 121 and 3443 are palindromic numbers. How many 5 digit palindromic numbers are there?
  1. So, a 5-digit palindromic number is of the form: ABCBA where A,B, and C are digits.
  2. B and C can be any of 10 digits: 0-9
  3. A can't be a zero (think about it!)
  4. Therefore the number of 5-digit palindromic numbers is _______
5) Jolene and Troy open a corner cookie and juice stand. After the first week Jolene creates a bar chart showing how many of each kind of cookie they sold. They plan on selling 480 cookies the next week. How many chocolate nut cookies should they bake? Express your answer to the nearest dozen of cookies.
Count up the total chocolate nut cookies they made and divide it by the total number of cookies = ______________

Then multiply this fraction times the 480 they expect to make and divide by 12:


= ______ dozen chocolate nut cookes.