# Probability

Suppose that infants are classified as low birth weight if they have birth weight 2500g, and as normal birth weight if have birth weight 2501g. Suppose that infants are also classified by length of gestation in the following four categories: <20 weeks, 20-27 weeks, 28-36 weeks, >36 weeks. Assume the probabilities of the different period of gestation are as given in the table below:

See attached for table.

Also assume that the probability of low birth weight given that length of gestation is <20 weeks is .540, the probability of low birth weight given that length of gestation is 20-27 weeks is .813, the probability of low birth weight given that length of gestation is 28-36 weeks is .378, and the probability of low birth weight given that length of gestation is >36 weeks is .031.

a) What is the probability of having a low birth weight infant?

b) Show that the events {length of gestation 27 weeks} and {low birth weight} are not independent.

https://brainmass.com/statistics/probability/probability-460609

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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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