Question
A charity event offers a Money Game in which a bowl contains five balls. All of the balls are made of the same material and
A charity event offers a "Money Game" in which a bowl contains five balls. All of the balls are made of the same material and are equal in size, weight, and shape. Two of the balls are worth 5.49 dollars each, and three of the balls are worth y dollars, where y is an amount between 11.00 dollars and 24.99 dollars. Two balls are picked sequentially without replacement.
What is the probability that the second ball is worth 5.49 dollars?
If y=14.7, What is the expected value of the amount from the first ball picked?
What is the probability that the first ball is worth more than 10 dollars if the second ball is less than 10 dollars? If y=17.64, What is the probability that both balls' sum is at most 9.95 dollars?
Let D denote the difference between the two amounts picked. For example, if you pick a 5.49 dollar ball first and then a 15.49 dollar ball next, D is 10.00. If you pick a 15.49 dollar ball first and a 5.49 dollar ball next, D is also 10.00. If both balls are worth 5.49, then D is 0. If y=19.11, what is the expected value of D?
For a certain value of y, it turns out that E[D]=10.83 and E[D^2]=195.4815. What is the standard deviation of D?
For a certain value of y, it turns out that E[D]=10.62 and Var[D]=75.1896. What is the variance of 10*D?
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