Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2017 Grade 6 Probability & Statistics
Problem
Solution
1) A number is chosen at random from the set {1, 2, 3, ..., 49, 50}. What is the probability that the number is prime?
(express your answer as a fraction in lowest terms)

 1. Here are the prime numbers below 50:
    2 3 5 7 11 13 17 19 23 29 31 37 41 43 47
2. There are 15 of them.
2. Probability = 15/50 = 3/10
2) A dart is dropped and lands onto a random place on this target. Find the probability that the dart lands in a shaded region. This is actually a geometry problem.
1. Compute the area of the center square = 1 sq. ft.
2. Compute the area of the shaded ring as
    its outer dimensions squared -
    its inner dimensions squared =
    4 x 4 - 3 x 3 = 16 - 9 = 7 sq. ft.
3. Add these 2 together and divide by the area of the outer square = (7 + 1)/36 = 8/36 = 4/18 = 2/9

Problem
Solution
3) Two six-sided dice are rolled. What is the probability that the product of the two numbers will be greater than 18?
(express your answer as a fraction in lowest terms)		 Here is the table of the product of 2 dice: The probability of a product greater than 18 is
    8/36 = 4/18 = 2/9
4) Orrin decides to make bike license plates. His design will have a letter followed by 2 digits. For example he could make a license plate with Z05, or Q22. How many unique license plates can he make? 1. The number of letters is 26
2. The number of digits is 10 (0,1,2,3,4,5,6,7,8,9)
3. Multiply the number of possibilities of each of the 3 places together =
    26 x 10 x 10 = 2600
5) After 4 games, Naomi's average points per game is 17 points. After the 5th game, her average rose to 18 points per game. How many points did she score in the 5th game? 1. Let P4 be the sum of Naomi's scores for the first 4 games.
    P4 = 4 x 17 = 68
2. Let P5 be her score for the 5th game.
3. Then (P4 + P5)/5 = 18
4. Solve for P5 =
    (68 + P5)/5 = 18
    68 + P5 = 90
    P5 = 90 - 68 = 22