proabability

**tukker0509** · October 11th 2012, 12:04 PM

The probability of an event and its complement equals one. True or false?

**Plato** · October 11th 2012, 12:31 PM

Originally Posted by tukker0509

The probability of an event and its complement equals one. True or false?

$\mathcal{P}(E)+\mathcal{P}(E^c)=\mathcal{P}(E)+[1-\mathcal{P}(E)]=~?$

**jsweston828** · October 11th 2012, 12:50 PM

Originally Posted by Plato

$\mathcal{P}(E)+\mathcal{P}(E^c)=\mathcal{P}(E)+[1-\mathcal{P}(E)]=~?$

What is that equation????!

**Plato** · October 11th 2012, 01:19 PM

Originally Posted by jsweston828

What is that equation????!

Does the OP mean

$\mathcal{P}(E)+\mathcal{P}(E^c)$ OR $\mathcal{P}(E\cap E^c)~?$

**jsweston828** · October 11th 2012, 01:20 PM

Im so confused! I just answered True!!

**Plato** · October 11th 2012, 01:23 PM

Originally Posted by jsweston828

Im so confused! I just answered True!!

Well $\mathcal{P}(E)+\mathcal{P}(E^c)=1$ AND $\mathcal{P}(E\cap E^c)=0.$

**jsweston828** · October 11th 2012, 01:27 PM

So would you say the answer is true or false!!

**Plato** · October 11th 2012, 01:33 PM

Originally Posted by jsweston828

So would you say the answer is true or false!!

I have no idea. "The probability of an event and its complement equals one."
That is such a poorly constructed phrase as to be meaningless.
Look at reply #4. It could be either.

**jsweston828** · October 11th 2012, 01:34 PM

ohhh I see! Im just going to hope its correct!

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