Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2006 Grade 5 Probability & Statistics

Problem
Hint
1) How many people must be present in a room in order to be 100% certain that two people in the room celebrate their birthdays in the same month? 1. In the worst case, every one in the room has a birthday in a different month up to ____ people.
2. After that, the next one surely has a birthday in a month that someone else has. That number (the next one) is the ____th person.

2) The table shows the results of many spins that Jules made with a spinner. Based on these results, what is the probability that Jules's spinner will land on the apple on his next spin? Express your answer as a fraction in lowest terms.
1. Compute the total number of spins = ____
2. Use this to compute the probability of it landing on apple = ____
3) Sidney took a survey of her fellow campers at summer camp and wants to show the results in a bar graph. She accidentally forgot to put the bar corresponding to redheads on the graph, but she correctly showed all other colors. If 50% of the campers have brown hair, 25 campers have brown hair, 5 campers have green hair, and 10 campers have black hair, how many of the campers have red hair? Fill in a bar for the redheads on the graph. 1. 50% of the campers have brown hair and there are ____ brown haired campers, then there are a total of ____ campers.
2. Subtract the number of campers that have hair other than red from this total.
    There are ____ redheads.

Problem
Hint
4) If 2 regular six-sided dice are tossed at the same time, what is the probability that the sum of the 2 dice will be less than or equal to 4? Fill out this table and answer the question.
Probability of a sum less than or equal to 4 is ____
5) You are the manager of the girls' basketball team. The championship game is coming up, and the coach has asked you to determine from his statistics which of his top three players has the best record for free throws. The statistical information you have is:
Joy made 21 out of her last 25 free throws.
Mary made 17 out of her last 20 free throws.
Nancy made 12 out of her last 15 free throws.
Tell the manager the order of his top 3 players: who is first, who is second, and who is third.
1. Compute the percentage of successful free throws for each girl.
2. Order them from best down.
3. _____ is first, _____ is second and _____ is third.