Analyzing the Sample Space

Oct 13, 2025 by miodeya.com 59 views

Introduction

In this article, we will delve into a mathematical problem involving a pair of cards and a six-sided die. Richard has a red card and a black card, and he randomly selects one of the cards. After that, he rolls a six-sided die. We will analyze the sample space of the event and determine the correct answer from each drop-down menu.

Understanding the Problem

Richard has two cards: a red card (R) and a black card (B). He randomly selects one of the cards, and then he rolls a six-sided die. The sample space of the event is listed as follows:

Card Selected	Die Rolled
R	1
R	2
R	3
R	4
R	5
R	6
B	1
B	2
B	3
B	4
B	5
B	6

Analyzing the Sample Space

The sample space consists of 12 possible outcomes: 6 outcomes when the red card is selected and 6 outcomes when the black card is selected. Each outcome is a combination of the card selected and the number rolled on the die.

Calculating the Probability

To calculate the probability of each outcome, we need to determine the total number of possible outcomes. Since there are 2 cards and 6 possible outcomes for each card, the total number of possible outcomes is 2 x 6 = 12.

The probability of each outcome is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. For example, the probability of selecting the red card and rolling a 1 is 1/12, since there is only 1 favorable outcome (R, 1) out of 12 possible outcomes.

Determining the Correct Answer

Based on the sample space and the probability calculations, we can determine the correct answer from each drop-down menu.

Card Selected

Red Card (R): 6/12 = 1/2
Black Card (B): 6/12 = 1/2

Die Rolled

1: 2/12 = 1/6
2: 2/12 = 1/6
3: 2/12 = 1/6
4: 2/12 = 1/6
5: 2/12 = 1/6
6: 2/12 = 1/6

Conclusion

In this article, we analyzed the sample space of the event and determined the correct answer from each drop-down menu. We calculated the probability of each outcome and determined the probability of selecting the red card and rolling a 1, 2, 3, 4, 5, or 6. We also determined the probability of selecting the black card and rolling a 1, 2, 3, 4, 5, or 6.

Recommendations

Based on the analysis, we recommend the following:

When selecting the card, choose the Red Card (R) with a probability of 1/2.
When rolling the die, choose the number 1, 2, 3, 4, 5, or 6 with a probability of 1/6.

Final Thoughts

Q: What is the sample space of the event?

A: The sample space of the event consists of 12 possible outcomes: 6 outcomes when the red card is selected and 6 outcomes when the black card is selected. Each outcome is a combination of the card selected and the number rolled on the die.

Q: How do I calculate the probability of each outcome?

A: To calculate the probability of each outcome, you need to determine the total number of possible outcomes. Since there are 2 cards and 6 possible outcomes for each card, the total number of possible outcomes is 2 x 6 = 12. The probability of each outcome is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

Q: What is the probability of selecting the red card and rolling a 1?

A: The probability of selecting the red card and rolling a 1 is 1/12, since there is only 1 favorable outcome (R, 1) out of 12 possible outcomes.

Q: What is the probability of selecting the black card and rolling a 6?

A: The probability of selecting the black card and rolling a 6 is 1/12, since there is only 1 favorable outcome (B, 6) out of 12 possible outcomes.

Q: Can I use a calculator to calculate the probabilities?

A: Yes, you can use a calculator to calculate the probabilities. Simply enter the number of favorable outcomes and the total number of possible outcomes, and the calculator will give you the probability.

Q: How do I determine the correct answer from each drop-down menu?

A: To determine the correct answer from each drop-down menu, you need to calculate the probability of each outcome and choose the one with the highest probability.

Q: What is the probability of selecting the red card and rolling a number between 1 and 6?

A: The probability of selecting the red card and rolling a number between 1 and 6 is 6/12 = 1/2, since there are 6 favorable outcomes (R, 1), (R, 2), (R, 3), (R, 4), (R, 5), and (R, 6) out of 12 possible outcomes.

Q: What is the probability of selecting the black card and rolling a number between 1 and 6?

A: The probability of selecting the black card and rolling a number between 1 and 6 is 6/12 = 1/2, since there are 6 favorable outcomes (B, 1), (B, 2), (B, 3), (B, 4), (B, 5), and (B, 6) out of 12 possible outcomes.

Q: Can I use a probability chart to determine the correct answer?

A: Yes, you can use a probability chart to determine the correct answer. A probability chart is a table that shows the probability of each outcome. You can use the chart to determine the correct answer from each drop-down menu.

Q: How do I create a probability chart?

A: To create a probability chart, you need to list all the possible outcomes and their corresponding probabilities. You can then use the chart to determine the correct answer from each drop-down menu.

Conclusion

In this article, we answered frequently asked questions about the sample space of the event and determined the correct answer from each drop-down menu. We calculated the probability of each outcome and determined the probability of selecting the red card and rolling a 1, 2, 3, 4, 5, or 6. We also determined the probability of selecting the black card and rolling a 1, 2, 3, 4, 5, or 6.