Scott Myers is a security analyst for a sell-side firm who covers Intuit

Scott Myers is a security analyst for a sell-side firm who covers Intuit (ticker INTU). Scott believes that its stock price will be considerably affected by the condition of credit flow in the economy. Based on data from previous periods, Scott also estimates that the probability that the stock price of Intuit goes up is 0.90 when there is significant improvement in credit flow in the economy, 0.40 when there is marginal improvement in credit flow in the economy, and 0.10 when there is no improvement in credit flow in the economy. Scott consults with Wendy Arnold, the firm’s economics analyst, who estimates that the probability is 0.20 that credit flow will improve significantly, 0.50 that it will improve only marginally, and 0.30 that it will not improve at all.

a. Based on these estimates, what is the probability that the stock price of Intuit goes up?

b. A week later, Scott emails Wendy that the stock price of Intuit has gone up significantly. Since public data about credit flows is routinely delayed, Wendy wants to write a note to her investment clients about current credit flows. What is the probability that credit flow in the economy has improved significantly?