Re: probability question

That is what I am confused with ...

To get the Pr of low BW, I think I need to use:
Pr(AUBUCUD) = Pr(A)+Pr(B)+Pr(C)+Pr(D)
- P(A&B) - P(A&C) - P(A&D) - P(B&C) - P(B&D) - P(C&D)
+ P(A&B&C) + P(A&B&D) + P(A&C&D) + P(B&C&D)
- P(A&B&C&D)

If I use use the conditional Pr for for 20-27 weeks:
Pr(B|A) = Pr(AnB) / Pr(A) = Pr(B)
= (0.0001*0.54)/0.0001 = 0.54
this means that it is "independent"....

thx

Kevin E. Thorpe wrote:
Ethan.Johnsons@xxxxxxxxx wrote:
I am trying to figure out the probability of having a low birth-weight
infant, but it puzzles me.

Length of gestation Pr of Length of gestation Pr of Low
birth-weight
<20 weeks 0.0001
0.54
20-27 weeks 0.0059
0.813
28-36 weeks 0.0855
0.379
36 weeks 0.9082 0.35

So, I have:

where Pr(A) = <20 weeks = 0.54; Pr(B) = 20-27 weeks = 0.813;
Pr(C) = 28-36 weeks = 0.379; Pr(D) = >36 weeks = 0.35

Pr(AUBUCUD) = Pr(A)+Pr(B)+Pr(C)+Pr(D)-Pr(AnBnCnD)
= (0.54+0.813+0.379+0.35)-(0.54*0.813*0.379*0.35)
= 2.023

but, this gives 202.3%, which is obvisouly wrong.

If I do Pr(AnBnCnD), it will give 0.058, which is reasonably low.

What am I missing here?

How do you prove that the events {length of gestation is equal or less
than 27 weeks} and {low birth-weight} are not independent? By looking
at them, they are related.

thx much

Try looking at conditional probability. For example if A is the event
"low birth weight" then P(A|<20 wk gest) = 0.54. This may not
help with your immediate question, but it should help you sort
out the information given.

--
Kevin E. Thorpe
Assistant Professor, Department of Public Health Sciences
Faculty of Medicine, University of Toronto

.

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