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Assume we roll a fair four-sided die marked with 1, 2, 3 and 4. (a) Find...

Assume we roll a fair four-sided die marked with 1, 2, 3 and 4.
(a) Find the probability that the outcome 1 is first observed after 5 rolls.
(b) Find the expected number of rolls until outcomes 1 and 2 are both observed.
(c) Find the expected number of rolls until the outcome 3 is observed three times.
(d) Find the probability that the outcome 3 is observed exactly three times in 10 rolls
given that it is first observed after 5 rolls.
(e) Find the probability that the outcome 3 is first observed after 5 rolls given that
it is observed exactly three times in 10 rolls

Math   Statistics-And-Probability   
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