Toss a fair coin twice. You win $4 if both one Head and one Tails appears,...

  

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Toss a fair coin twice. You win $4 if both one Head and one Tails appears, lose $4 if no toss comes out Heads, and win or lose nothing otherwise. (a) What is the expected number of games you need to play to win once? (b) Assume that you play this game 100 times. What is, approximately, the prob- ability that you win at least $228.28? (c) Again, assume that you play this game 100 times. Compute (approximately) the amount of money x such that your winnings will be at least x with probability 0.5. Then, do the same with probability 0.975. Toss a fair coin twice. You win $4 if both one Head and one Tails appears, lose $4 if no toss comes out Heads, and win or lose nothing otherwise. (a) What is the expected number of games you need to play to win once? (b) Assume that you play this game 100 times. What is, approximately, the prob- ability that you win at least $228.28? (c) Again, assume that you play this game 100 times. Compute (approximately) the amount of money x such that your winnings will be at least x with probability 0.5. Then, do the same with probability 0.975.