# mutually exclusive event vs independent event

Can you illustrate with examples, what is "mutual exclusive event" and what is "independent event". Without math equations, please elaborate it..

• You must have some thoughts. What do you think "mutually exclusive" means?
– 5xum
Nov 6 '14 at 10:47
• When one event occurs other wont occur for mutually exclusive case.I wanted to see a practical analogy. Nov 6 '14 at 11:00

If I roll a die and toss a coin

• "The coin shows head" and "The coin shows tails" are mutually exclusive
• "The die shows 6" and "the die shows 3" are mutually exclusive
• "The die shows a perfect square number" and "The die shows a prime" are also mutually exclusive
• "The coin shows head" and "The die shows a 5" are independent
• "The die shows a prime number" and "The die shows an even number" are neither mutually exclusive nor independent
• "The die shows a 7" and "The coin shows head" are both mutually exclusive and independent.
• The last bullet is very much wrong- die shows 7 ?? What is meant by die shows 7? "Die shows 7" is not an event. One can ask the probability of an event from the sample space. In fact there is no such event which is both mutually exclusive and independent. Nov 5 '15 at 10:40

You have a string with $n$ bits each of which is either set to 1 or 0 w.p. $\frac{1}{2}$ respectively. If $j^{\text{th}}$ bit is set to 0 it can't be be set to 1 too - these events are mutually exclusive.

The probability to setting $(j+1)^{\text{th}}$ bit to either value doesn't change/depend on $j^{\text{th}}$ bit - hence the events are independent.

Events which are occur in same sample space has the following characters

• mutually exclusive

• mutually exhaustive

• equally likely

And

• sum of all events probablities equal to 1

Independent events are `not belongs to the same sample space and they are connected to different sample spaces

And if some events probabilities are equal , they from same sample space are said to be equally likely

But If they are independent and event probabilities are equal , they are not said to be equally likely

Instead of examples or formulas I'd go for a textual description. Events are independent if the fact that one of them occurs does not change your estimate about whether the other one also occurs. Mutual exclusive events are, in some sense, the total opposite since once you know that one of them occurs you can immediately deduce that the other one does not, so your estimate clearly changes. (Yes, I am aware of the fact that if one has 0 probability to begin with and the other has probability 1 they are both independent and mutually exclusive, hence the "in some sense" disclaimer)