I play a gambli ng game in which I will win k 2 dollars with probability 1/2

Question:

I play a gambli ng game in which I will win k −2 dollars with probability 1/2for any k ∈ N , that is,

  • With probability 1/2, I lose 1 dollar;
  • With probability 1/4, I win 0 dollar;
  • With probability 1/8, I win 1 dollar;
  • With probability 1/16, I win 2 dollars;
  • With probability 1/32, I win 3 dollars;

What is the probability that I win more than or equal to 1 dollar and less than 4 dollars?

What is the probability that I win more than 2 dollars?

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