The Table Gives A Set Of Outcomes And Their Probabilities. Let $A$ Be The Event the Outcome Is A Divisor Of 6. Find $P(A$\].$\[ \begin{tabular}{|c|c|} \hline Outcome & Probability \\ \hline 1 & 0.17 \\ \hline 2 & 0.4 \\ \hline

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Introduction

In probability theory, the probability of an event is a measure of the likelihood of that event occurring. Given a set of outcomes and their corresponding probabilities, we can calculate the probability of any event by summing the probabilities of the outcomes that make up that event. In this article, we will explore how to find the probability of an event given a table of outcomes and their probabilities.

The Table of Outcomes and Their Probabilities

The following table gives a set of outcomes and their corresponding probabilities:

Outcome Probability
1 0.17
2 0.4
3 0.12
4 0.05
5 0.02
6 0.24

Defining Event A

Let AA be the event "the outcome is a divisor of 6." This means that event AA consists of the outcomes that are divisors of 6, which are 1, 2, and 6.

Calculating the Probability of Event A

To find the probability of event AA, we need to sum the probabilities of the outcomes that make up event AA. In this case, the outcomes that make up event AA are 1, 2, and 6, with probabilities 0.17, 0.4, and 0.24, respectively.

# Define the probabilities of the outcomes that make up event A
prob_1 = 0.17
prob_2 = 0.4
prob_6 = 0.24

# Calculate the probability of event A
prob_A = prob_1 + prob_2 + prob_6

Solving for P(A)

By summing the probabilities of the outcomes that make up event AA, we can calculate the probability of event AA as follows:

# Calculate the probability of event A
prob_A = prob_1 + prob_2 + prob_6
print("P(A) =", prob_A)

Conclusion

In this article, we have explored how to find the probability of an event given a table of outcomes and their probabilities. We have defined event AA as the event "the outcome is a divisor of 6" and calculated the probability of event AA by summing the probabilities of the outcomes that make up event AA. The probability of event AA is given by the sum of the probabilities of the outcomes 1, 2, and 6, which is 0.81.

Final Answer

The final answer is 0.81\boxed{0.81}.

Discussion

The probability of event AA is a measure of the likelihood of the outcome being a divisor of 6. In this case, the probability of event AA is 0.81, which means that there is an 81% chance that the outcome will be a divisor of 6.

Related Topics

  • Probability theory
  • Event probability
  • Outcome probability
  • Divisors of 6

References

  • [1] Probability theory, Wikipedia
  • [2] Event probability, Wikipedia
  • [3] Outcome probability, Wikipedia
  • [4] Divisors of 6, Wikipedia
    The Table of Outcomes and Their Probabilities: A Q&A Guide ================================================================

Introduction

In our previous article, we explored how to find the probability of an event given a table of outcomes and their probabilities. We defined event AA as the event "the outcome is a divisor of 6" and calculated the probability of event AA by summing the probabilities of the outcomes that make up event AA. In this article, we will answer some frequently asked questions (FAQs) related to the topic.

Q&A

Q: What is the probability of event A?

A: The probability of event AA is 0.81, which means that there is an 81% chance that the outcome will be a divisor of 6.

Q: What are the outcomes that make up event A?

A: The outcomes that make up event AA are 1, 2, and 6.

Q: How do I calculate the probability of event A?

A: To calculate the probability of event AA, you need to sum the probabilities of the outcomes that make up event AA. In this case, the outcomes that make up event AA are 1, 2, and 6, with probabilities 0.17, 0.4, and 0.24, respectively.

# Define the probabilities of the outcomes that make up event A
prob_1 = 0.17
prob_2 = 0.4
prob_6 = 0.24

# Calculate the probability of event A
prob_A = prob_1 + prob_2 + prob_6

Q: What is the formula for calculating the probability of an event?

A: The formula for calculating the probability of an event is:

P(A) = P(outcome 1) + P(outcome 2) + ... + P(outcome n)

where P(outcome i) is the probability of outcome i.

Q: How do I determine the outcomes that make up an event?

A: To determine the outcomes that make up an event, you need to identify the possible outcomes that satisfy the condition of the event. In this case, the event is "the outcome is a divisor of 6", so the outcomes that make up event AA are 1, 2, and 6.

Q: What is the difference between an event and an outcome?

A: An event is a set of outcomes that satisfy a certain condition, while an outcome is a single result of an experiment or trial.

Q: How do I calculate the probability of an event given a table of outcomes and their probabilities?

A: To calculate the probability of an event given a table of outcomes and their probabilities, you need to sum the probabilities of the outcomes that make up the event.

Conclusion

In this article, we have answered some frequently asked questions (FAQs) related to the topic of finding the probability of an event given a table of outcomes and their probabilities. We have provided examples and formulas to help you understand the concept and calculate the probability of an event.

Final Answer

The final answer is 0.81\boxed{0.81}.

Discussion

The probability of an event is a measure of the likelihood of that event occurring. In this case, the probability of event AA is 0.81, which means that there is an 81% chance that the outcome will be a divisor of 6.

Related Topics

  • Probability theory
  • Event probability
  • Outcome probability
  • Divisors of 6

References

  • [1] Probability theory, Wikipedia
  • [2] Event probability, Wikipedia
  • [3] Outcome probability, Wikipedia
  • [4] Divisors of 6, Wikipedia