# Probability

[1] On a recent English test, students were given the names of four authors and four novels (one author one title), and asked to match each novel, with the correct author. If a student just guesses randomly, what is the probability of getting zero, one, two, three or four correct?

[2] You are to select two cards one at a time from a well-shuffled deck of 52 playing cards (jokers not allowed). You want to get a heart as the first card and a King (K) as the second.

If you are given the following two options to do this, which option would you choose,

Option #1: to be allowed to select the first card and put it back into the deck before selecting the second card, or

Option #2: to be allowed to keep the first card (not to put it back to the deck) and select the second one?

a) Explain why you think your choice is better.

b) What is the probability to select such two cards under option #1?

c) What is the probability to select such two cards under option #2?

d) Does your choice from a) agree with the results from b) and c)? Explain.

https://brainmass.com/math/probability/probability-233019

#### Solution Summary

This provides examples of working with probabilities regarding cards and matching.

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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