Homework Sourse1 Suppose PA 025 PB 04 and PBA 02 What is the value of PA
1. Suppose P(A) = 0.25, P(B) = 0.4, and P(B|A) = 0.2. What is the value of P(A|B)?
2. You are choosing among four investment plans. The payoffs of these investment plans depends on next year’s sales (see the table below.) You believe that next year’s sales will either decrease or increase. We also know that the sales will increase with a probability of 0.7.
Sales decrease
Sales increase
Plan 1
$8,500
$12,000
Plan 2
$6,000
$14,500
Plan 3
$10,000
$10,500
Plan 4
$10,100
$10,200
a. Which alternative should be chosen based on the maximin criterion?
b.Which alternative should be chosen based on the minimax regret criterion?
c. Which alternative should be chosen based on expected value criterion?
d. Which alternative should be chosen based on maximax criterion?
| Sales decrease | Sales increase | |
| Plan 1 | $8,500 | $12,000 |
| Plan 2 | $6,000 | $14,500 |
| Plan 3 | $10,000 | $10,500 |
| Plan 4 | $10,100 | $10,200 |
Solution
1. P(A) = 0.25, P(B) = 0.4, and P(B|A) = 0.2.
Then the value of P(A|B) is 0.25/0.4=0.625
2.a.The maximin criterion is plan 4 $10,100
b.The minimax regret criterion is plan 1 $6,000
c.The expected value criterion is plan 3 $ 10000
d.The maximin criterion is plan 2 $14,500.
