# Problem 8. 20 pts] I have a special coin with "memory" that I will be tossing...

###### Question:

Problem 8. 20 pts] I have a special coin with "memory" that I will be tossing ezactly once every day for the next 4 days (so tomorrow will be day 1). Let p, denote the probability that the coin shows up heads when it's tossed on day i (this means it shows up tails with probability 1 -pi when tossed on day i). Did I mention the coin has "memory"? By that I mean that: 1. On day 1, the coin is equally likely to show up as heads or tails, i.e. p 1/2 2. For every subsequent day i, i > 1, p 0.1 if the coin toss on day i 1 resulted in heads, and p P-1+0.1 if the coin toss on day i - 1 resulted in tails. What is the probability that the coin toss on day 4 results in heads? Hint: Use the tree method and/or the law of total probability.

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