Your friend is in the market for a used car. He is considering two options for a very similar car - (A) buying from a dealership that costs $10,000, and (B) buying from a private seller that costs $9,000. He believes that the car in the dealership is in perfect condition. He believes that the one from the private seller may have a frame damage with a probability (p) of 0.25. He estimates that repairing the frame damage would cost $3,000. He can buy a Carfax report that will accurately (perfect information) tell whether the car has a frame damage or not.

b. The cost for Carfax report is $30. The expected value of information in the report depends on your friend's assessment of the probability (p) of frame damage. Determine the range of p for which the report is worth $30.