Geometry Probability--Using Tree Diagrams & Area Models

Leslie is playing the "Pick a Marble" game. A bag contains one red, one white, and one brown marble. Each marble has an equal chance of getting chosen. Leslie reaches in, picks a marble, notes its color, and returns it to the bag. She then picks another marble out of the bag and notes its color. The tree diagram shows the sample space for a first and second selection of the marble. How many different outcomes are there with two marble selections?

• 3

• 9

• 12

• none of the above

Refer to the "Pick a Marble" tree diagram. What is the probability Leslie will choose two white marbles? Enter your answer as a percentage rounded to the nearest tenth.

Refer to the "Pick a Marble" tree diagram. What is the probability Leslie will choose at least one brown marble? Express your answer as a percentage rounded to the nearest tenth.

Refer to the "Pick a Marble" tree diagram. What is the probability Leslie will not choose any red marbles? Express your answer as a percentage, rounded to the nearest tenth of a percent.

Refer to the "Pick a Marble" tree diagram. What is the probability Leslie will choose two marbles of the same color? Express your answer as a percentage, rounded to the nearest tenth of a percent.

A game consists of two spinners. Spinner #1 consists of the colors green, blue, and red. The spinner has a 1/3 chance of landing on any color in Spinner #1. Spinner #2 also consists of colors green, blue, and red. On that spinner, green has a 1/2 chance of being landed on, blue has a 1/4 chance, and red has a 1/4 chance. Refer to the diagram, which shows an area model of the sample space. What fractions should represent the boxes containing A, B, and C?

• $A=\frac{1}{9}\ \ B\ =\ \frac{1}{9}\ \ \ C\ =\ \frac{1}{9}$

• $A=\frac{1}{6}\ \ \ \ \ \ B\ =\ \frac{1}{6}\ \ \ \ \ \ C\ =\ \frac{1}{6}$
  

• $A=\frac{1}{3}\ \ \ \ B\ =\ \frac{1}{6}\ \ \ \ \ C\ =\ \frac{1}{6}$

• $A=\frac{1}{6}\ \ \ \ B\ =\ \frac{1}{9}\ \ \ \ \ C=\frac{1}{12}$

A game consists of two spinners. Spinner #1 consists of the colors green, blue, and red. The spinner has a 1/3 chance of landing on any color in Spinner #1. Spinner #2 also consists of colors green, blue, and red. On that spinner, green has a 1/2 chance of being landed on, blue has a 1/4 chance, and red has a 1/4 chance. Refer to the diagram, which shows an area model of the sample space. What is the probability of getting red on both spins?  Express answer as a percentage, rounded to the nearest tenth.

In the "Pick a Number" game, there is a bag containing the numbers 1, 2, 3, 4, 5, 6, 7 with one number on each tile. There is a second bag containing the numbers 8, 10, 12, 13, 16. A player randomly selects a tile from the first bag and then a tile from the second bag. The player wins the game if they select two odd number tiles. Use any appropriate strategy to determine the probability of winning the game. Express your answer as a percentage rounded to the nearest tenth.