The owner of a small business has the right to have a retail stall at a large festival to be held during the summer. She judges that this would either be a success or a failure and that the probability that it is a success is 0.4. If the stall was a success, the net income from it would be £90,000. If the stall was a failure, there would be a net loss of £30,000 from it. To help to make the decision, the owner could pay for market research. This would cost £5,000. The market research will either give a positive indication or a negative indication. The conditional probability that it gives a positive indication, given that the stall will actually be a success, is 0.75. The conditional probability that it gives a positive indication, given that the stall will actually be a failure, is 1/3.

The owner has various options:

• Do nothing.
• Go ahead without market research.
• Pay for the market research.
• Sell her right to a stall for £10,000.
If she pays for the market research then, depending on the outcome, she can:
• Do nothing more.
• Go ahead.
• Sell her right to a stall. If the market research gave a positive indication the price would be £35,000. If the market research gave a negative indication the price would be only £3,000.

What should she do?