Mutually Exclusive Events and Independent Events

[safirshahbaaz90]

Hi Tommy,

I find it hard to identify mutually exclusive events and independent events. In fact, the definitions of the 2 sound the same to me. I have tried several sources but I still get confused.

Could you please help with these 2 concepts with an example. Question 19 in Probability in the 5 lb book says the events are independent. But doesn't picking 1 chip without replacement increase the odds of picking the other? :(

Please help!!

Regards,
Safir

[tommywallach]

Hey Safir,

No GRE questions actually use that language, and I've never even thought about it. So honestly, I wouldn't worry about what it means, given that it isn't relevant.

In the question you cited, yes the first pick affects the other one. I don't see anywhere in that question or it's explanation the term "independent" event, so I'm not sure where you're seeing that...

-t

[safirshahbaaz90]

Hi Tommy,

The Manhattan Word Problem guide mentions that for "AND" problems, the 2 events must be independent and for "OR" problems, they must be mutually exclusive. I was assuming that since we multiplied the quantities in the problem, the events must be independent.

Is this assumption correct?

Regards,
Safir

[tommywallach]

Hey Safir,

All it means is that if you're going to add two quantities in an OR situation, there can't be a situation where both of them happen. For example:

If I say the only possible weather possibilities are rain and snow, and there is a 50% chance of it raining and a 50% chance of it snowing, does that mean there's a 100% chance of rain OR snow? No, because there could be rain AND snow. The only way you're allowed to add them is if they are mutually exclusive.

As for independent, as far as I know, all variables are independent in probability, so don't worry about that either.

-t

[safirshahbaaz90]

OK :) Thanks a lot Tommy :)

Regards,
Safir

[tommywallach]

Glad to help.

(Also, realized my explanation was a little bit unclear. What I meant was that there isn't a 100% chance of rain or snow occurring alone, because that would ignore the possibility of both happening.)

-t