Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2013 Grade 7 Probability and Statistics
Problem
Hint
1) Gino's Pizzeria makes One Price personal pizzas for which you have a choice of one sauce, one vegetable, and one meat. They have 3 different sauces, 5 different vegetables choices, and 5 different meat choices. All come with delicious cheese. How many different versions of the One Price personal pizzas are there? Multiply all the choices together to get the total number of versions of the pizza = _____ versions.

2) A full deck of Rook cards consists of cards numbered 1-14 in four different colors plus one special Rook card for a total of 57 cards. Assume the deck is well shuffled. What is the probability of drawing first the Rook and then a 14 followed by a 13 of the same color? You may leave your answer as a product of reduced fractions or as a decimal out to 6 decimal places.
  1. Probability of drawing the Rook card = ________

  2. Probability of drawing a 14 = _________

  3. Since the drawing of the 14 established the color and there is only ____ of same color then the probability of getting a 13 of the same color is __________ because there are ___ remaining cards to select from.

  4. Total probability = _______

Problem
Hint
3) At the beginning of each school year, Joey and Mateo's mom marks off their heights on the kitchen wall. Joey measures the gaps showing annual growth and plots them by the grade level. He notices he grew more between kindergarten and 1st grade than Mateo by an inch. Which boy has the higher average annual growth and by how much? Round to the nearest tenth of an inch.
  1. Add up Joey's yearly growths and divide by the number of years to get his average growth =


    _______
  2. Do the same for Mateo = ______ inches/year.

  3. _____ has the higher growth rate by _____ inch.

4) Molly had a 16 points-per-game average over the first 7 games of the season. In the last five games Molly has scored 28, 16, 20, 24, 18 points respectively. What was her final-points-per game average? Round to the nearest point.

 Add up all of Molly's scores (including those in the first 7 games) and divide by the number of scores =


_____ per game.
5) On St. Patrick's day the Leprechaun Bakery sells Lucky Cakes. These cakes are precut into 1 in x 2 in rectangles and one of the pieces has a Lucky Penny hidden in it. Mom is considering the 4 in x 8 in cake and the 9 in x 12 in larger cake. What is the ratio of the probabilities of getting the piece with the Lucky Penny in the smaller cake to getting the piece with the Lucky Penny in the larger cake? Express your answer as a reduced fraction.
  1. # pieces of the smaller cake = _____ pieces

  2. # pieces of the larger cake = _____ pieces

  3. Divide the probability of getting a lucky penny with the smaller cake by the probability of getting it in the larger cake = ______