Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2008 Grade 7 Probability and Statistics
Problem
1) A basketball team was practicing their shots. Each player took five shots. Michael made 100% of his shots, while Steve only made 40%. If John made 3 shots, David made 2 and Brett made 1, what is the team's average of all the shots taken?

2) Most Washington license plates consist of a set of three numbers followed by a set of three letters. A witness sees a suspicious car and reports it to the police. He says the first two numbers were 4 and 6 but he missed the last one and the first letter was C. How many possible license plates does that describe?

3) A dart hits the dartboard shown at random. The board is a square and the horizontal lines are equally spaced. Find the probability of the dart landing in the shaded region.

Problem
4) A company manufactures washers that are supposed to be 2 mm thick. In reality they will accept washers that are within 1 mm of the 2 mm target. The company buys a new machine to produce these washers. Out of the first 100 washers it produces, the median thickness is 2.5 mm, the range is 3.9 mm, the first quartile is 1.8 mm, and the third quartile is 3 mm. The thickest washer had a thickness of 5 mm. From this data at least how many washers of the 100 washers did not meet the company's requirements?
5) Joan and David invent a probability game for a homework project that has players flip a fair coin and roll a fair 6 sided number cube with the numbers 1 through 6 on it. David moves ahead on the game board as many spaces as the number that comes up on the number cube when the coin lands on heads. Joan moves ahead three spaces when the coin lands on tails no matter what number comes up on the cube. After 2 rolls and flips what's the probability that David will have moved 8 spaces?