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

[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.

 

[mfb]

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.

 

[parshyaa]

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

 

[mfb]

What is the condition for independent events?

 

[parshyaa]

What is the condition for independent events?

That is what i am asking?

 

[mfb]

Definitions are something you should look up.