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I met the question in my exam:

flip one coin, the probability of head is 1/3, Pr{tail} = 2/3. Flip the coin twice, what are the four possible outcomes and their probabilities?

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2 Answers 2

Head Head 1/3 * 1/3 = 1/9
Head Tail 1/3 * 2/3 = 2/9
Tail Head 2/3 * 1/3 = 2/9
Tail Tail 2/3 * 2/3 = 4/9

By the way, the results of 1st and 2nd flips are independent.

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Head Head: 1/3 * 1/3 = 1/9
Head Tail: 1/3 * 2/3 = 2/9
Tail Head: 2/3 * 1/3 = 2/9
Tail Tail: 2/3 * 2/3 = 4/9
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