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Consider an experiment of tossing a coin repeatedly until the outcomes of two consecutive tosses are the same. If the probability of a random toss resulting in head is 1/3, then the probability that the experiment stops with head is

1. 1/3
2. 5/21
3. 4/21
4. 2/7

Correct answer: 5/21

Solution

The experiment stops when two consecutive tosses are the same. For the experiment to end with a head, the sequence must be a tail followed by a head, followed by another head. Using the given probability of heads (1/3) and tails (2/3), the total probability is calculated as (2/3) × (1/3) × (1/3) = 5/21.

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