Economists forecast that there is a 40% chance that we will have an economic boo

Question

Economists forecast that there is a 40% chance that we will have an economic boom next year and a 60% chance that we will have a recession. If the economy is good (economic boom), there is a 50% chance that the stock market will go up, a 30% chance of a normal stock market, and a 20% chance of a large drop in the stock market. If the economy is bad, there is a 20% chance that the stock market will go up, a 30% chance of a normal stock market, and a 50% chance of a large drop in the stock market. What is the probability of the stock market going up next year?

1. 20%.

2. 50%.

3. 32%.

Explanation / Answer

Economists forecast that there is a 40% chance that we will have an economic boom next year and a 60% chance that we will have a recession. If the economy is good (economic boom), there is a 50% chance that the stock market will go up, a 30% chance of a normal stock market, and a 20% chance of a large drop in the stock market. If the economy is bad, there is a 20% chance that the stock market will go up, a 30% chance of a normal stock market, and a 50% chance of a large drop in the stock market. What is the probability of the stock market going up next year?

1. 20%.

2. 50%.

3. 32%.

B=Boom

P( B) =0.4   P(B’)=0.6

P( UP/B) =0.5    P( UP/B’) =0.2  

P( UP) = P( UP/B)* P( B)+ P( UP/B’)* P(B’)

=0.5*0.4+0.2*0.6

=0.20+0.12

=0.32 or 32%

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