Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2010 Grade 6 Probability & Statistics
Problem
Solution
1) A secret agent is being flown by helicopter over the city block pictured with just a top view. She needs to land on one of the buildings but, because of wind and lack of experience, where she'll land is a random event. What is the probability she will land on a building roof?
1. Compute the areas of all the buildings, add them together:
    500 x 200 + 200 x 100 + 300 x 200 + 300 x 600 =
    360,000 sq. ft.
2. Divide this by the area of the block to get the probability =
    360,000/960,000 = 37.5% = 3/8

2) Louisa just had to try Bertie Bott's Every Flavored Beans. Her box had: 6 pickle flavored, 12 Grass flavored, 2 Chocolate flavored, 9 Earwax flavored, and 4 Sardine flavored. She eats three of them. What is the probability that the third one she eats is chocolate given that the first two were not chocolate? Express your answer as a reduced fraction. 		1. Compute the total number of beans in her box: 33
2. Subtract 2 = 31
3. Divide the number of chocolate beans by this number =
    2/31

3) The scores for an amazingly charmed basketball team are:
    110, 96, 124, 130, and 105.
They are about to play again and a psychic predicts their average after the game will be 115 points. If he is right, what will be the score for this game? 		Let S5 = the sum of the first 5 games.
S = score of the 6th game
1. Then (S5 + S)/6 = 115.
2. Solve this for S = (565 + S)/6 = 115
    565 + S = 690
    S = 125

Problem
Solution

4) On the first five 20 point quizzes Toni scores: 15, 4, 16, 18 , and 15. What are the possible quiz scores for the next quiz that would keep the median the same but raise Toni's average? Quiz scores are whole number. 		1. Rewrite the scores in order:
    4 15 15 16 18
2. Find the median = 15
3. The average is (4 + 15 + 15 + 16 + 18)/5 = 13.6
4. The next score will make the number of scores even, so the median is the average of the middle 2. This cannot be greater than 15 or the median will be the average of 15 and 16, so the only possible score that keeps the median the same and increases his average are 14 or 15

5) You are given the scrabble letter tiles that spell TRAVEL. How many four letter arrangements can you make with your tiles that have the pattern consonant, vowel, consonant, vowel? The arrangements need not spell a real word though many will.
(Note: since they are tiles you can use a letter only once.) 		1. There are 2 vowels and 4 consonants in TRAVEL.
2. There are 4 ways to choose the first consonant.
3. There are 2 ways to choose the first vowel.
4. There are 3 ways to choose the second consonant after you have chosen the first one.
5. There is 1 way to choose the last vowel after you choose the first vowel.
6. Muliply these to get the answer:
    4 x 2 x 3 x 1 = 24