PROBABILITIES PROBLEM

[ELENIG344]

Hi all!

I have a tough time with probability problems and was wondering if you could help me. Suppose there are four possibilities; Jill will get job A but not B, Jill will get job B but not A, Jill will get both jobs, Jill will get neither job.

Are the following formulas correct?

P(A or B) = P(A not B) + P(B not A) - P(both)

P(neither A nor B) = 1 - P(A or B)

1 = P(A not B) + P(B not A) + P(neither A nor B) + P(both)

And how can the last formula be correct? If we substitute the first formula into the second, the result indicates that the third formula is incorrect, right?

Thank you!!

[Sage Pearce-Higgins]

And how can the last formula be correct? If we substitute the first formula into the second, the result indicates that the third formula is incorrect, right?

I agree, there's an inconsistency going on here. This isn't really a probability issue, so much as a set issue. I agree with your definition of the four possibilities: Jill will get job A but not B, Jill will get job B but not A, Jill will get both jobs, Jill will get neither job. Actually, if you haven't seen the double-set matrix, I strongly suggest that you check out the Word Problems section of our guide and get familiar with this. You're far more likely to see this situation with numbers (check out PS 6 from the Diagnostic Test at the front of the OG), although the scenario could involve probability too, so I'll follow through on your analysis.

Since these 4 outcomes cover all the possibilities, then they must sum to 1, so that
P(A not B) + P(B not A) + P(both) + P (neither) = 1

Be really careful with your definitions: P(A or B) probably means P(A not B) + P(B not A) + P(both), so your first formula is most likely inaccurate. I might put this instead:
P(just one of A or B) = P(A not B) + P(B not A) - P(both)

On a wider point, there's little point in memorizing formulas that you don't understand well. Much more important is the ability to understand new situations and organize your logic.