# Can E1 and E2 be both independent and mutually exclusive events?

• I
• parshyaa
In summary, the conversation discusses the difference between independent events and mutually exclusive events. It provides an example of rolling a die and calculating the probabilities of two events, E1 and E2, and the intersection of E1 and E2. It also mentions that being mutually exclusive does not necessarily mean that the events are independent, and prompts the question of what condition defines independence.
parshyaa
Can you give a example to differentiate independent events from mutually exclusive events?

Suppose there is a random experiment of rolling a die:

E1 is a event of getting a multiple of 3
E1={3,6}
E2 is a event of getting a multiple of 2
E2={2,4,6}
Is E1&E2 are independent events, here they are not mutually exclusive.

parshyaa said:
Is E1&E2 are independent events, here they are not mutually exclusive.
Calculate the probability of E1, E2 and "E1 and E2" and check it yourself?

Finding two mutually exclusive events should be easy.

mfb said:
Calculate the probability of E1, E2 and "E1 and E2" and check it yourself?

Finding two mutually exclusive events should be easy.
P(E1)=1/3, P(E2)= 1/2
P(E1∩E2) = 1/6
This only tells me that they are not mutually exclusive
This does not tell me any thing about independent event

What is the condition for independent events?

mfb said:
What is the condition for independent events?
That is what i am asking?

Definitions are something you should look up.

## 1. What is probability?

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 representing impossibility and 1 representing certainty.

## 2. How is probability calculated?

The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

## 3. What is the difference between theoretical and experimental probability?

Theoretical probability is based on mathematical calculations and assumes that all outcomes are equally likely. Experimental probability is based on actual data collected from experiments or observations.

## 4. What are independent and dependent events?

Independent events are those that are not affected by the outcome of other events. Dependent events are those that are affected by the outcome of other events.

## 5. How is probability used in real life?

Probability is used in many different fields, including science, economics, and statistics. It is used to make predictions, assess risks, and make informed decisions based on data. Some common applications of probability include weather forecasting, stock market analysis, and medical diagnoses.

• General Math
Replies
13
Views
3K
• General Math
Replies
1
Views
2K
• Precalculus Mathematics Homework Help
Replies
7
Views
4K
• General Math
Replies
2
Views
2K
• Quantum Physics
Replies
108
Views
6K
• Quantum Interpretations and Foundations
Replies
15
Views
2K
• General Math
Replies
1
Views
2K
• Quantum Physics
Replies
33
Views
2K
• Set Theory, Logic, Probability, Statistics
Replies
6
Views
2K
• General Math
Replies
2
Views
2K