Page 11 Example: Assume that business conditions in any year can be classified a
ID: 2932254 • Letter: P
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Page 11 Example: Assume that business conditions in any year can be classified as either good or bad. Suppose that if business is good this year, then it it will be also good next year with probability 0.7. Also suppose that if business is bad this year, then with probability 0.4 it will be good next year. The prpbability that business will be good this year is 0.6, Find the probability that the following statements are true 1. 2. 3. 4. 5. Business conditions both this year and next year will be good. Business conditions will be good this year and bad next year. Business conditions will be bad both years. Business conditions will be good next year. Given that business conditions are good next year, what is the probability that they were good this year?Explanation / Answer
let condition good is represented by G1 and G2 for first and second year and G1c,G2c is bad for first and second year.
1) business condition is good for both year =P(G1)*P(G2|G1) =0.6*0.7 =0.42
2) probability that this will be good this year and bad next year =P(G1)*P(G2c|G1) =0.6*(1-0.7)=0.18
3)probability =P(G1c)*P(G2c|G1c)=(1-0.6)*(1-0.4) =0.24
4)probability =P(G2) =P(G1)*P(G2|G1)+P(G1c)*P(G2|G1c) =0.6*0.7+0.4*0.4=0.58
5)P(G|G2) =P(G1)*P(G2|G1)/P(G2) =0.6*0.7/0.58=0.7241
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