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?

Answer 1

Number of sample space = 6

Given that 2 appears on the k^th roll of the die.

So first (k – 1)^th roll have 5 outcomes each and k^th roll results 2

i.e. only 1 outcome.

∴ Number of element of sample space correspond to the event that 2 appears on the k^th roll of the die = `5^(k - 1)`.