We are looking to find $P(G \mid U)$, the probability the economy grows given that ABC stock is up.

• $P(G) = \text{probability the economy grows} = 0.50$
• $P(R) = \text{probability of a recession} = 0.50$
• $P(U) = \text{probability the stock is up} = 0.375$

Using Bayes' formula:

$$P(G \mid U) = P(G) \times P(U \mid G) / P(U)$$ $$P(G \mid U) = (0.50) \times (0.60) / 0.375$$ $$P(G \mid U) = 0.3 / 0.375 = 0.8 = 80.0\%$$

(Book 2, Module 12.2, LO 12.g)