Probability inequality : Is the following always true?

In summary, probability inequality is the concept that the likelihood of an event occurring can range from impossible to certain. It is always true and is calculated by dividing the number of desired outcomes by the total number of possible outcomes. It is closely related to probability distribution and cannot be used to predict the outcome of a single event.
  • #1
michonamona
122
0

Homework Statement



P(AUB) <= P(A) + P(B)

Homework Equations





The Attempt at a Solution



I can't understand the intuition behind this property. It's not a homework assignment, it was just something that came up in class.

Thanks,
M
 
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  • #2
Go back to the definition, how was P(A) defined for you.
 
  • #3
Have you covered the Addition Rule yet? If so, compare what you wish to show to that.
 

1. What is probability inequality?

Probability inequality refers to the concept that in any given situation, the likelihood of an event occurring can range from impossible (probability of 0) to certain (probability of 1).

2. Is probability inequality always true?

Yes, probability inequality is a fundamental principle in probability theory and is always true. It is based on the fact that every event has a certain probability of occurring, and therefore, the inequality always holds.

3. How is probability inequality calculated?

Probability inequality is calculated by dividing the number of desired outcomes by the total number of possible outcomes. This gives a decimal number between 0 and 1, which can then be converted to a percentage to represent the probability of the event occurring.

4. What is the relationship between probability inequality and probability distribution?

Probability inequality is closely related to probability distribution, as it is used in the calculation of probabilities for different outcomes in a distribution. In probability distribution, the total probability of all possible outcomes is always equal to 1, which is a manifestation of probability inequality.

5. Can probability inequality be used to predict the outcome of a single event?

No, probability inequality cannot be used to predict the outcome of a single event. It only provides a likelihood or chance of an event occurring, but it does not guarantee the actual outcome. Probability inequality is based on the law of large numbers, which requires a large number of trials to accurately predict the outcome of an event.

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