WASHINGTON STATE MATHEMATICS COUNCIL - 1997 MIDDLE SCHOOL MATH OLYMPIAD

7TH GRADE PROBABILITY & STATISTICS - SCHOOL ___________________________ TEAM_______

1. Out of a bag with 10 colored cubes we drew 10 times, but each time we drew one out, we replaced it before we drew again. After 10 drawings we counted 4 red (R) cubes and 6 green (G) cubes. On the second round of 10 draws there were 3 R and 7 G. The third round had 5 R and 5 G. The 4^{th} round saw 3 R and 7G. The 5^{th} round of 10 had 5 R and 5 G. The 6^{th} round showed 1 R and 9 G. The last round was 7 R and 3 G. Mathematically, the probability shown through the draws matched the 10 cubes. How many red cubes are there out of the 10 cubes?

Answer: ________________

2. A gum-ball machine contains nine red, seven white, and eight green gum balls. What is the least amount of gum balls that a person needs to buy in order to be sure that they get four of the same color?

Answer: ________________

3. The ordered list of numbers 18, 21, 24, a, 36, 37, b has a median of 34 and a mean of 35. What is the difference between a and b?

Answer: ________________

4. Eighty students went on a field trip to Seattle. 36 students visited the aquarium, 30 went to the Woodland Park Zoo, and 33 went to the Science Center. 17 students went to both the aquarium and the zoo. 11 went to both the zoo and the Science Center and 15 went to both the Science Center and the aquarium. 8 students went to all three. How many students did not go to any of the three?

Answer: ________________

5. Of the counting numbers from 1 through 100, what should the 10's digit be to find the lowest probability of finding a prime number? (Assume the numbers 1-9 are preceded by a 0.)

Answer: ________________