# Comparing the Probability of Events: Is the Difference Greater Than Expected?

• pivoxa15
In summary, the conversation discusses the probability of four events, with events 1 and 2 having probabilities of 0.81 and 0.82 respectively, while events 3 and 4 have probabilities of 0.01 and 0.02. The question is whether event 4 is more likely to occur than event 3 and whether event 2 is more likely to occur than event 1. The comparison is "the more likely" and the question is rephrased as whether the likelihood of event 4 over event 3 is greater than the likelihood of event 2 over event 1. The response confirms that event 4 has twice the probability of event 3 and event 2 has a slightly higher
pivoxa15
If two events 1 and 2 have probability 0.81 and 0.82

And another two events, 3 and 4 have probability 0.01 and 0.02

Would it be correct to say that (event 4 will occur more often than event 3), compared with (event 2 more likely to occur than even 1)?

The comparison is 'the more likely'. To repharase the question. Is the (likliness of event 4 over event 3) greater than the likliness of (event 2 over event 1)?

I hope this question makes sense.

Last edited:
Yes, you are definitely correct.

Event 4 has exactly twice the probability of Event 3.
Event 2 has almost the same probability as Event 1.

Event 4 over Event 3 = 2/1
Event 2 over Event 1 = 82/81

Hope that helps.

Simon

Last edited:

Yes, it would be correct to say that event 4 will occur more often than event 3 and that event 2 is more likely to occur than event 1. The difference in probabilities between events 3 and 4 is much greater than the difference between events 1 and 2. In other words, the likelihood of event 4 occurring is greater compared to the likelihood of event 3 occurring, compared to the likelihood of event 2 occurring compared to the likelihood of event 1 occurring. This can also be seen by the fact that the probabilities for events 3 and 4 are much smaller than the probabilities for events 1 and 2.

## 1. What is the purpose of comparing the probability of events?

The purpose of comparing the probability of events is to determine if there is a significant difference between the expected outcome and the actual outcome. This allows researchers to make conclusions about the effectiveness of a particular treatment or intervention.

## 2. How is the difference between expected and actual probability calculated?

The difference between expected and actual probability is calculated by subtracting the expected probability from the actual probability. This difference is then compared to a predetermined threshold to determine if it is statistically significant.

## 3. What is a p-value and how does it relate to comparing probability?

A p-value is a statistical measure that represents the probability of obtaining a result at least as extreme as the one observed, assuming the null hypothesis is true. In comparing probability, the p-value is used to determine if the difference between expected and actual probability is greater than expected by chance.

## 4. What are some common methods for comparing probability?

Some common methods for comparing probability include chi-square tests, t-tests, and ANOVA (analysis of variance). These methods use statistical calculations to determine if the observed difference in probability is statistically significant.

## 5. Are there any limitations to comparing probability?

Yes, there are limitations to comparing probability. These include the assumption of independence between events, the need for a large sample size, and the potential for confounding variables. It is important for researchers to carefully consider these limitations when interpreting the results of a comparison of probability.

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