Question

Marcus and his brother always argue about who will walk the dog. Their father wants to find a random way of deciding who will do the job. He invented a game to help them decide. Each boy will have a bag with three colored blocks in it: one yellow, one green, and one white. Each night before dinner, each boy draws a block out of his bag. If the colors match, Marcus walks the dog. If the two colors do not match, his brother walks the dog. Marcus's father wants to be sure that the game is fair. a. Make a probability tree of all of the possible combinations of draws that Marcus and his brother could make. How many possibilities are there? b. What is the probability that the boys will draw matching blocks?

Answer 1

By studying the experiment, we will see that:

a) There are 9 possible outcomes (listed in the answer) all with the same probability.

b) The probability of drawing matching blocks is 1/3.

How to know if the game is fair?

The game is fair if and only if the two outcomes have the same probability.

Here the two outcomes that we care for are:

• The colors match.
• The colors do not match.

a) First, in each bag all the blocks have the same probability of being drawn, which is 1/3.

Then each combination will have the same probability, which is:

p = (1/3)*(1/3) = 1/9.

Now, the possible combinations of colors are given by the table:

Marcus    Brother    probability

yellow      yellow            1/9

yellow      green             1/9

yellow      white              1/9

white       yellow            1/9

white       green             1/9

white       white              1/9

green     yellow            1/9

green     green             1/9

green     white              1/9

b) The probability that the boys draw matching blocks is given by the sum between the probabilities that they draw 2 yellow blocks, 2 green blocks, and 2 white blocks, this is:

P = 1/9 + 1/9 + 1/9 = 1/3.

If you want to learn more about probability, you can read:

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