To be a winner in a certain game, you must be successful in three successive rounds. The game depends on the value of U, a uniform random variable on (0,1). If U > .1, then you are successful in round 1; if U > .2, then you are successful in round 2; and if U > .3, then you are successful in round 3.
(a) Find the probability that you are successful in round 1.
(b) Find the conditional probability that you are successful in round 2 given that you were successful in round 1.
(c) Find the conditional probability that you are successful in round 3 given that you were successful in rounds 1 and 2.
(d) Find the probability that you are a winner.
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