Stats Problem

Stamkos1992

Stamkos1992

Member
Can anyone help me help with this---> 1. Let A and B be two events defined on a sample space S. If the probability that at least one of them occurs is 0.3 and the probability that A occurs but B does not occur is 0.1, what is P(B) ?

 
wait isn't this really easy?

Because the probability of A, B or both is

P(AuB)=P(A)+P(B)-P(AnB)=0.3

and the probability of A occurring but not B would be:

P(A)-P(AnB)=0.1

so solving both sides for P(A) I got

P(A)= 0.3-P(B)+P(AnB)

P(A)= 0.1+P(AnB)

so

0.3-P(B)+P(AnB)=0.1+P(AnB)

0.3+P(AnB)-0.1-P(AnB)=P(B)

0.2=P(B)

Basically what I am saying there is that if the probability of A or B or both is 0.3 and the probability of A alone is 0.1 then the probability of B alone or both must equal 0.2.

 
I dunno though I could have somehow in that math came to the incorrect conclusion that A and B are mutually exclusive since P(A) would equal 0.1 and therefore P(AnB) would be zero.

I hope that's the right answer but it's late and could be more complicated than I thought
 
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