Section B Section B Checkpoint

Problem 1

A cube is labeled so that when it is rolled, it shows only 1, 2, or 3 with equal chances of each one coming up. This cube is rolled, then 2 different coins are flipped.

How many outcomes are in the sample space? Explain your reasoning.
What is the probability that the cube shows 2, and the coins land showing the same face? Explain your reasoning.

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Solution

12. Sample reasoning: The outcomes are 1HH, 1HT, 1TH, 1TT, 2HH, 2HT, 2TH, 2TT, 3HH, 3HT, 3TH, 3TT.
$\frac{2}{12}$ or equivalent. Sample reasoning: There are 2 outcomes that match the situation: 2HH and 2TT. There are 12 outcomes in the sample space, so the probability is $\frac{2}{12}$ .

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Sample Response

12. Sample reasoning: The outcomes are 1HH, 1HT, 1TH, 1TT, 2HH, 2HT, 2TH, 2TT, 3HH, 3HT, 3TH, 3TT.
$\frac{2}{12}$ or equivalent. Sample reasoning: There are 2 outcomes that match the situation: 2HH and 2TT. There are 12 outcomes in the sample space, so the probability is $\frac{2}{12}$ .

Problem 2

A computer game shows that opening a prize box has a 25% chance that it contains your favorite character to play in the game.

How could you use coins to simulate opening 3 prize boxes to find the probability of getting your favorite character?

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Solution

Sample response: Flip 2 coins three times to simulate opening 3 boxes. If both coins show heads any of the times, then it represents getting my favorite character. To find the probability, repeat this process many times and find the fraction of times this happens.

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Sample Response