math

In old gangster movies on TV, you often hear of "number runners" or the "numbers racket." This numbers game, which is still played today, involves betting $1 on the last three digits of the number of stocks sold on a particular day in the future as reported in The Wall Street Journal. If the payoff is $900, what is the expectation for this numbers game?

A realtor who takes the listing on a house to be sold knows that she will spend $900 trying to sell the house. If she sells it herself, she will earn 6% of the selling price. If another realtor sells a house from her list, the first realtor will earn only 3% of the price. If the house remains unsold after 6 months, she will lose the listing. Suppose that probabilities are as follows:
Event Probability
Sells the house alone 0.50
Sells through another agent 0.40
Does not sell in 6 months 0.10
What is the expected profit from listing a $175,000 house?

In a certain school, the probabilities of the number of students who are reported tardy are shown in the following table:
Number tardy: 0 1 2 3 4
Probability: 0.19 0.26 0.29 0.22 0.04
What is the expected number of tardies (rounded to two decimal places)?

Calculate the expectation (to the nearest cent) for the Reader's Digest sweepstakes described. Assume there are 187,000,000 entries.

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