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Consider an unending sequence of independent trials where each trial

Consider an unending sequence of independent trials, where each trial is equally likely to result in any of the outcomes 1, 2, or 3. Given that outcome 3 is the last of the three outcomes to occur, find the conditional probability that

(a) The first trial results in outcome 1;

(b) The first two trials both result in outcome 1.

(a) The first trial results in outcome 1;

(b) The first two trials both result in outcome 1.

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