Mutally Exclusive

[quaidy4]

Let A and B be two events defined on a sample space S. Suppose that P(A) = 0:4 and
P(B) = 0:8. Is it possible to say whether or not A and B are mutually exclusive? Justify
your answer.

I know that mutually exclusive means that its impossible for them both to occur at the same time.

Therefore I think that the answer is no, because the ratio of P(A) 0:4 and P (B) 0:8 would not be able to occur in both events but, Im not really sure how they got the ratio of 0:4 and 0:8 I just kinda guess on this one! I know how to figure it out if they gave you an A B and C but since they only gave you an A and B Im fairly confused.

 

[pka]

Let A and B be two events defined on a sample space S. Suppose that P(A) = 0:4 and P(B) = 0:8. Is it possible to say whether or not A and B are mutually exclusive? Justify
your answer.

This must be true: \(\displaystyle 1\ge\mathcal{P}(A\cup B)=\mathcal{P}(A)+\mathcal{P}(B)-\mathcal{P}(A\cap B).\)
Is that possible if \(\displaystyle \mathcal{P}(A\cap B)= 0~?\)

 

[quaidy4]

I don't really understand that though, I understand the formula and such but I don't understand how you would determine if it's possible or not when only given 2 numbers.

 

[pka]

I don't really understand that though, I understand the formula and such but I don't understand how you would determine if it's possible or not when only given 2 numbers.

What does \(\displaystyle \mathcal{P}(A)+\mathcal{P}(B)=~?\)
Remember that \(\displaystyle 1\ge\mathcal{P}(A\cup B)\)
How can you make that happen unless \(\displaystyle \mathcal{P}(A\cap B)>0~?\)

 

[quaidy4]

thanks I understand it now!