a) What is the probability that it will come up tails? b) John offers you the following game. If the coin comes up tails, he pays you $1.50. If it comes up heads, you pay him $1.00. How much on the average will you win or lose each time you play this game (or what is the expected value of this game)?
| x | p(x) |
| 0 | .2 |
| 1 | .2 |
| 2 | .2 |
| 3 | .2 |
| 4 | .2 |
8. The game show Deal or No Deal features 26 suitcases with various amounts of money. The contestant chooses one than then begins to open the others. At the end of each round, the «Banker» makes an offer to end the game. The game ends either when the player takes the offer, or when he or she has opened all 25 suitcases that he or she did not choose, in which case he or she gets the amount in the chosen suitcase.
Suppose that the player has four suitcases left with the following amounts in them: $1,000,000, $100,000, $1000, and $100. What would the fair offer for the contestant to quit be from the «Banker»?
a) Suppose we use this rule to provide two outcomes. If the outcomes are independent, what is the probability that the first one will be a 4 and the second will be a 1? b) What is the probability that at least one of the two outcomes will be a 1?
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