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Question
An experiment consists of rolling a die until a 2 appears. How many elements of the sample space correspond to the event that the 2 appears on the kth roll of the die?
Solution
Number of sample space = 6
Given that 2 appears on the kth roll of the die.
So first (k – 1)th roll have 5 outcomes each and kth roll results 2
i.e. only 1 outcome.
∴ Number of element of sample space correspond to the event that 2 appears on the kth roll of the die = `5^(k - 1)`.
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