Bayes Theorem

[R111]

Hi All,

Question in a practice exam:

P(G) = probability of economy growing = 50%
P(R) = probability of economy in recession = 50%
P(U) = probability of ABC stock going up = 37.5%

The question is what's the probability of the economy growing given the stock going up.

The answer is

P(G I U) = P(G) x P(U I G) / P(U)
P(G I U) = 0.5 x 0.6 / 0.375

How do you get 0.6?

Thanks
David

 

[Dr.Peterson]

Did you quote the entire problem exactly? I don't see how they can ask this without giving any conditional (or combined) probabilities at all. We know nothing about how these events interact. It isn't even certain that G and R are intended to be complementary, though one might assume that. Or is this asked in a context where some knowledge of economics is assumed?

 

[R111]

Here is the exact question word for word:

An analyst determines that there is a 50% chance the economy will grow and that there is a 50% chance the economy will go into recession. There is also a 37.5% chance that ABC stock will rise in price. Given that ABC stock has risen in price, what tis the probability the economy has grown.

A. 30%
B. 50%
C. 70%
D. 80%

I have however the same reasoning as you. I think they have left out something but wanted a second opinion


and the answer sheet gives (word for word) :

we are looking to find P(G I U)

P(G) = probability of economy growing = 50%
P(R) = probability of economy in recession = 50%
P(U) = probability of ABC stock going up = 37.5%

Using Bayes' formula:

P(G I U) = P(G) x P(U I G) / P(U)
P(G I U) = 0.5 x 0.6 / 0.375
P(G I U) = 0.3 / 0.375 = 0.8 = 80%

 

[pka]

Here is the exact question word for word:

An analyst determines that there is a 50% chance the economy will grow and that there is a 50% chance the economy will go into recession. There is also a 37.5% chance that ABC stock will rise in price. Given that ABC stock has risen in price, what tis the probability the economy has grown.
A. 30%
B. 50%
C. 70%
D. 80%
I have however the same reasoning as you. I think they have left out something but wanted a second opinion

I agree with that & your work is correct. What we need now is \(\mathcal{P}(U|G)\) see if that somewhere.