# Probability Problems

## Question

1. Suppose all you have is a biased coin that when tossed comes up heads 60% of the time and tails 40% of the time. How can you use it to simulate a fair coin, i.e. one that comes up heads 50% of the time and tails 40% of the time? Explain why your method works.

2. Suppose all you have is a fair coin. How can you use it to simulate a biased coin such as the one in problem 1 that comes up heads 60% of the time and tails 40% of the time? Explain why your method works.

3. Suppose all you have is a fair coin. How can you use it to – completely accurately! –simulate a biased coin that has P (H)=1/√2 and P (T)=1− 1/√2 ? Explain why your method works, or explain why there can be no such method.
Note: Keep in mind that p12 is irrational (because √2 is), and so cannot be written as a ratio of integers. That makes this problem rather harder than 2...

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