Before a market study, there is a 70% chance that the market will be good.

When the market is good, the study has a track record of predicting a good market 85% of the time.

When the market is bad, the study has a track record of predicting a good market 20% of the time.

Given that the study has predicted a good market, what is the probability that the market is actually good?

Question

Before a market study, there is a 70% chance that the market will be good.

When the market is good, the study has a track record of predicting a good market 85% of the time.

When the market is bad, the study has a track record of predicting a good market 20% of the time.

Given that the study has predicted a good market, what is the probability that the market is actually good?

amistre64 · Answer

or rather:  .....what is the probability that the market will actually be good?

anonymous · Answer

baye's formula?

amistre64 · Answer

yep

amistre64 · Answer

i tend to do a table, rather than the formula itself ...

amistre64 · Answer

i get lost in the P(B|A')s and P(A|B)s and such lol

anonymous · Answer

actually that is always confusing. i am going to write down what i think the answer is, and then how i got it
i think it is 
$$\frac{.85\times .7}{.85\times .7+.2\times .3}$$

amistre64 · Answer

\begin{array}l
&&&&prior:&70\%&30\%\
&+&-&\
good\  markt&[85\%]&15\%&\
bad\  market&20\%&80\%&\
\end{array}

  .85*.70 = .5950 / X  <---
+.20*.30 = .0600
----------------
            X = .6550

P(answer) = .595/.060

yep, same answers :)

anonymous · Answer

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