What is the probability that the company will be profitable?

henribar

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Mar 8, 2016
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Values for company's projected profit and their associated probability: (x values in 1000s)
x-100050100150200
P(X=x)0.10.20.30.250.10.05

What is the probability that the company will be profitable?
I don't understand why my answer is not consistent.
Answer:
Pr(X>0)=Pr(X≥50) . <- Should be true
1-Pr(X
≤50)=1-Pr(X<50)
1-0.6 =1-(Pr(X
≤50)-Pr(X=5))
0.4=1-(1-0.6-0.3)
0.4=0.9
I'm not using the cdf properly in one or both cases but have no way of knowing. What is the correct answer?
 
Pr(X>0)=Pr(X≥50) . <- Should be true
Good.

1-Pr(X <= 50)=1-Pr(X<50)
Bad. There is a probability mass AT x = 50.

1-0.6 =1-(Pr(X <= 50)-Pr(X=5))
What? Why do we care about 5?

0.4=1-(1-0.6-0.3)
Pr(X=5) = 0

I'm delighted that you recognized this as incorrect.

You have every way of knowing the correct answer. Pr(X>0) = Pr(X = 50) + Pr(X = 100) + Pr(X = 150) + Pr(X = 200) -- Done.
Or, if you like, P(X>0) = 1 - [Pr(X=-100) + Pr(X=0)] -- Done again.
 
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