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1. A group of volleyball players consists of four Grade-11 students and six Grade-12 students. If six players are chosen at random to start a match, what is the probability that three will be from each grade?

2. If a bowl contains ten hazelnuts and eight almonds, what is the probability that four nuts randomly selected from the bowl will all be hazelnuts?

3. If you simultaneously roll a standard dice and spin a spinner with eight equal sectors numbered 1 to 8. What is the probability of both rolling an even number and spinning an odd number?

4. A bag contains three green marbles and four black marbles. If you randomly pick two marbles from the bag at the same time, what is the probability that both marbles will be black?

5. What is the probability of rolling a total of 7 in two rolls of a standard dice if you get an even number on the first roll?

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Probability cases are solved.

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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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