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Probability

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Employees of a company fall into four categories: Managers (4%),
Administrators (12%), Technicians (26%) and Labourers (58%).
If 20% of the Managers, 5% of the Administrators, 3% of the Technicians
and 0.5% of the Labourers have the opportunity of promotion in the next
year:
(i) What is the probability that a randomly chosen employee is a
manager and will gain promotion next year?
(ii) What is the probability that a randomly chosen employee will gain
promotion next year?
(iii) What is the probability that a randomly chosen employee is an
Administrator if the employee has the opportunity of gaining
promotion next year?

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The probability

A young engineer has invented holographic mobile phones and has approached a venture capital company to invest in it. The venture capital company considers the product to be an all or nothing product: either everyone will want one because everyone else has one or no one will want one because there will be no one to use it with. The company believes that the probability that it will take off netting them a profit of $2000000 is 0.14. If it doesn't take off then they expect that they would loose $200000. They are considering using a consumer survey to gather more information. However, the company has experience that shows that the probability that the consumer survey will predict success for a product that will fail is 0.24, and the probability that the consumer survey will predict failure when the product will be a success is 0.07. What is the monetary value of the information from a consumer survey to the venture capital company in this case? (ie what is the maximum that they should spend on a consumer survey)?

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