Probability

[osquare]

a store-bought pregnancy test produces a correct result 99% of the time when a woman is actually pregnant but is only 97% accurate when a woman is not pregnant. Assuming a woman has a 40% chance of actually being pregnant when she takes the test, and that the result comes out positive, what is the probability that she is actually pregnant

[Jackdaw33]

If the result is positive then it is 99 %.

[bobbinwales]

Id say its more tricky . My non maths but common sense answers 40 x0.99 + 60 x 0.03 whatever that gives.
Maybe around

[bobbinwales]

Ignore me. Di'nt see the positive result bit

[Gizmonster]

A long time since I've tried to tackle probabilities but I'd tackle it logically:
Assume 1000 women take the test.
40% of women are pregnant that take the test, so we have 600 not pregnant and 400 pregnant.
The test on the 600 non-pregnant women will give 582 negative and 18 positive results (97% accurate).
The test on the 400 pregnant women will give 396 positive and 4 negative results (99% accurate).
We have a total of 414 positive results and 396 of these are true positives.
So if a woman receives a positive result, the chance that she's actually pregnant is:
(396 / 414) x 100 = 95.65%

This is just my logical approach, so I could be wrong??

[bobbinwales]

Am still not sure I agree with jackdaws result as we after take account of it might be a false positive which occurs in 3% of cases when woman isnt actually pregnant.
95.65% pregnat

[bobbinwales]

drat!!.
Cant do maths but can do spreadsheets and I got

0.956521739 preggers

0.043478261 not pregnant

[Gizmonster]

//// 0.956521739 preggers

0.043478261 not pregnant ////

..... which agrees with my answer above :)

[bobbinwales]

Yes we agree. I just took to long to type it thinking no body else was interested
I did 0.99 x0.4
divided by 0.99x4+0.6*0.03
for pregnant.
Your way is much easier to follow and it would of been easier if I done it that way