Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2011 Grade 7 Probability and Statistics
Problem
Hint
1) At the local middle school math night, one game has a grand prize that everyone wants. To play and win you need to get three 6's. There are two options:
Option 1: roll a regular number cube with the numbers 1 to 6 on it three times and hopefully roll a 6 each time.
Option 2: pull three balls from a bin that contains 18 balls; each ball has one number on it and there are three balls for each number from 1 to 6.

Which option is better and why? Include the probabilities for both options in your answer.
  1. Probability #1: 3 6s with 3 rolls of a single die:
    Multiply the probability of rolling a 6 with one die times itself 3 times = ____________

  2. Probability #2: 3 balls from a bin:
    This is the same as the problem of selecting balls out of a jar without replacing the ball selected, so each pull has one less ball to pull from, so =

    _____________
  3. Option _____is the best

Problem
Hint
2) Lena is signing up for classes at her summer camp. She wants to take gymnastics, horseback riding, drawing, and theatre just like her friend Rhoda. Gymnastics and drawing are offered all four sessions. Horseback riding is offered session 2 and 3. Theatre is offered session 1 and 4. Campers take one class a session. She wants the same schedule Rhoda has; Gymnastics, drawing, horseback riding and theatre, in that order. If she is assigned randomly to a schedule that includes her four choices, what is the probability she will get the same schedule as Rhoda? Use G = gymnastics, D = drawing,
T = theatre and H = horseback riding.
The best way to do this is to list the possibilities. Here is a diagram of the 4 sessions, remembering that H is available only in sessions 2 and 3 and Theatre is available only in sessions 1 and 4:
Session 1Session 2Session 3Session 4
T or
G or D		H or
G or D		H or
G or D		T or
G or D

Use this table to list ALL the possibilities:
Be very careful that your possibilities fit the table above.
Session 1Session 2Session 3Session 4
    
    
    
    
     
    
    
    
    
    
 There are ____ ways to schedule the 4 classes , so the probability of Lena getting the same schedule as Rhoda is ________

Problem
Solution
3) Three cousins all have birthdays that fall on the 27th day of different months and none were born in a leap year. What is the probability of that happening? Express your answer as a fraction, you need not reduce it.
  1. Assume that the first cousin was born on the 27th. Then there are ____ 27ths out of ____ days in the year that he could have been born on.
  2. If the second cousin was born in a different month, then there are _____ days out of the year for his/her birthday
  3. That leaves ____ days out of the year for the last cousin's birthday, so, the probability of this happening is ...



    _____________
4) The Bin Candy Store has candy bins arranged along two walls. Along the first wall the price is $3.95 per pound. Along the second wall the price is $6.50 per pound. On Saturday the store sells 450 pounds from the first wall bins and 200 pounds from the second wall bins. What was the average cost in dollar per pound of candy sold on Saturday? Express your answer to the nearest cent. They sold a total of ___ pounds of candy at a total price of ______ which is = ____________ per pound.
5) Scientists are monitoring the population of a parrot species in a jungle. One day they catch and tag 50 parrots and release them. A week later they return and catch 50 parrots again and find that 15 of those parrots are tagged. Based only on this data, what is a good initial estimate for the population of this species of parrot in this jungle? Let X be the total population of parrots.
  1. _____ of the parrots in the second sample were tagged

  2. This fraction was ____ parrots, so

  3. X = _______ parrots total.