Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2007 Grade 8 Probability and Statistics

Problem
1) Roy is looking forward to making some good money once he's in high school. He does an informal survey of his older brother's friends. He puts the results of his survey in a table shown below. Compute the mean and median hourly wage for Roy's informal survey. Is Roy more likely to get a job that pays close to the mean hourly wage or to the median hourly wage? Explain.

2) Here's a game with one standard six sided die with the numbers 1 - 6. In at most three rolls of the die be the one to get as close to 10 as possible without going over. If you roll a 4 on the first roll, what's the probability you will go over 10 in the next two?

3) College bound high school students often take a foreign language. One school has a senior class of 255 students. 178 are college bound and they all take either French or Spanish. 97 students have taken at least 3 years of high school French, and 123 have taken at least 3 years of high schoolSpanish. No student has taken at least 3 years of both languages. If a student is selected at random, what's the probability they've had at least three years of French or Spanish but are not college bound?

Problem
4) A coin is weighted so that it comes up heads twice as often as tails. If it comes up heads 5 times in a row, what's the probability it will come up tails on the next toss?

5) Gavin had a GPA of 2.9 going into his last semester of 8th grade. He would like to bring it up to a 3.0 or higher. Each semester he has taken 6 classes and each one is worth 1 credit. His middle school is 6th through 8th for a total of 6 semesters. What's the lowest his last semester's GPA can be to get a cumulative GPA of 3.0?