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(b) With each sample point we'll associate a number of keys that we try until we find the one that opens the door. In the case of H (i.e the first key fits) X = 1; for MH (first key doesn't fit, the second key fits) X = 2; for MMH X = 3 and for MMMH X = 4.
(c) For the first sample point we can choose any of the four keys, the probability of the right choice:
For the second sample point we choose first an incorrect key (M) and then one of the three remaining keys,
In the same way