An investment company analyses stocks and predicts whether their price will go up or down. So far, half of the stocks analysed by the company have gone up, 3/4 of the stocks that went up were correctly predicted to go up, and 2/5 of the stocks that went down were incorrectly predicted to go up. Suppose that the company tells you that it will go up. Compute the probability that the stock will indeed go up.
My Solution:
Let A denotes "Stock will go up "
Let B denotes "Company tells that the stock will go up"
Now, we need to find P(A | B)
P(A|B)= P(B|A).P(A)/P(B)
P(B) = P(B|A).P(A) + P(B|A').P(A') = (3/4)(0.5) + (2/5)(0.5)
Please tell me if this is correct.