There are only 100 tickets available to be sold in this lottery
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There are only 100 tickets available to be sold in this lottery

1. You buy a lottery ticket to a lottery that costs $10 per ticket. There are only 100 tickets available to be sold in this lottery. In this lottery there are one $500 prize, two $100 prizes, and four $25 prizes. Find your expected gain or loss.

2. Complete the PDF and answer the questions.


a. Find the probability that x = 2.

b. Find the expected value.

3. Suppose that you are offered the following "deal.” You roll a die. If you roll a six, you win $10. If you roll a four or five, you win $5. If you roll a one, two, or three, you pay $6.

a. What are you ultimately interested in here (the value of the roll or the money you win?

b. In words, define the Random Variable X.

c. List the values that X may take on.

d. Construct a PDF.

e. Over the long run of playing this game, what are your expected average winnings per game?

f. Based on numerical values, should you take the deal? Explain your decision in complete sentences.

4. A venture capitalist, willing to invest $1,000,000, has three investments to choose from. The first investment, a software company, has a 10% chance of returning $5,000,000 profit, a 30% chance of returning $1,000,000 profit, and a 60% chance of losing the million dollars. The second company, a hardware company, has a 20% chance of returning $3,000,000 profit, a 40% chance of returning $1,000,000 profit, and a 40% chance of losing the million dollars. The third company, a biotech firm, has a 10% chance of returning $6,000,000 profit, a 70% of no profit or loss, and a 20% chance of losing the million dollars.

a. Construct a PDF for each investment.

b. Find the expected value for each investment.

c. Which is the safest investment? Why do you think so?

d. Which is the riskiest investment? Why do you think so?

e. Which investment has the highest expected return, on average?

5. Suppose that 20,000 married adults in the United States were randomly surveyed as to the number of children they have. The results are compiled and are used as theoretical probabilities. Let X = the number of children married people have.


a. Find the probability that a married adult has three children.

b. In words, what does the expected value in this example represent?

c. Find the expected value.

d. Is it more likely that a married adult will have two to three children or four to six children? How do you know?

Hint
StatisticsInvestment is an asset or item that is purchased with the hope of it generating profits and income. It is the allocation of money in expectation of it appreciating in value in the future. It allows an individual to generate additional income and grow one’s wealth....

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