Type the correct answer in each box.
There are three letter tiles—A, B, and C—in a bag, and there are three number tiles—1, 2, and 3—in another bag. Alexis picks a letter tile, and she picks a number tile. Complete the table representing the sample space for this situation.
Letter Tile
A B C
Number Tile 1 A-1 B-1 C-1
2 A-2 C-2
3 A-3 B-3
The sample size of the event is .
Answer (2)
Complete the table by filling the missing entry with C-3.
Determine the sample size by counting all possible outcomes.
There are 3 possible number tiles and 3 possible letter tiles, resulting in 3 Ă— 3 = 9 outcomes.
The sample size of the event is 9 ​ .
Explanation
Analyze the problem We are given a table representing the sample space of picking a letter tile (A, B, C) and a number tile (1, 2, 3). The table is partially filled, and we need to complete it and find the sample size.
Complete the table The missing entry in the table corresponds to picking the number tile 3 and the letter tile C. Therefore, the missing entry should be C-3.
Determine the sample size To find the sample size, we count the total number of possible outcomes in the sample space. Each cell in the table represents a unique outcome. The completed table will have the following entries:
A
B
C
1
A-1
B-1
C-1
2
A-2
B-2
C-2
3
A-3
B-3
C-3
There are 3 rows and 3 columns, so there are a total of 3 Ă— 3 = 9 possible outcomes.
State the final answer The sample size of the event is 9.
Examples
This type of problem is useful in probability and statistics when you want to understand all possible outcomes of an experiment. For example, if you were designing a game with different character and weapon combinations, you could use a sample space to list all possible combinations and their probabilities. This helps in balancing the game and ensuring fair chances for all players. Understanding sample spaces is also crucial in fields like genetics, where you might want to analyze all possible combinations of genes.
To find the sample size of the event, we complete the table with the missing entry C-3. There are a total of 9 possible combinations of letter and number tiles, making the sample size 9. The sample size of the event is 9 ​ .
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