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3 companies
the probanility that there profit will increase is
companyA 0.70
companyB 0.50
companyC 0.65
what is the probability that at least on company shows a profit increase?
so far i have only figured out that the probability that all will increase in profit is 0.23%
how do you get the at least one part
The probability of alternative occurance states: the probability that one or the other or both of two events will occur is equal to the probability that the first will occur, plus the probability that the second will occur, minus the probability that they both occur. (The final term in this formula provides a necessary correction because we have already counted the joint occurrence twice, once in each of the other terms.)
P(A V B) = P(A) + P(B) - P(A · B)
In this case we have three events. So we do it twice.
The probability that A or B will happen is A + B - A*B or .7 +.5 - (.7*.5) or .85 now we do it again with the result and C
so .85 + .65 - (.85*.65) or 0.9475
Prob (at least one shows a profit increase) = 1 - Prob(none shows a profit increase)Quote:
Originally Posted by kelsey
Prob(none shows a profit increase) = 0.3*0.5*0.35 = 0.0525
So Prob(at least one shows a profit increase) = 0.9475.
This assumes that the three companies show profits independently from one another. E.g. they shouldn't be in the same town or industry or be run by the same person.
so anytime that the question says at least one you can use this formula
hpe, that was pretty slick.
And yes whenever the question says "at least one" you can use this type of argument.