Question: 6. Random Questions (15 points)

1. [5 Points] What is the probability that the digit 1 doesn't appear among n digits where each digit is one of (0-9) and all sequences are equally likely?
2. [5 Points] Suppose you randomly permute the numbers 1, 2, ... ,11, (where 11 > 500). That is, you select a permutation uniformly at random. What is the probability that the number 3 ends up in the 130-th position in the resulting permutation? (For example, in the permutation 1, 3,2, 5,4 of the numbers 1... 5, the number 2 is in the 3rd position in the permutation and the number 4 is in the 5th position.)
3. [5 Points] A fair coin is flipped it times (each outcome in {H, Tr is equally likely). What is the probability that all heads occur at the end of the sequence? (The case that there are no heads is a special case of having all heads at the end of the sequence, i.e. 0 heads.)

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