An experiment consists of rolling die until a 2 appears. How many elements of the sample space correspond to the event that 2 appears on the kth roll of the die? How many element of the sample space correspond to the event that 2 appears not later than the kth roll of the die?

Explanation

To solve the problem step by step, we will break it down into two parts as presented in the question.

### Part 1: Finding the number of elements in the sample space when 2 appears on the kth roll.

1. **Understanding the scenario**: We are rolling a die until a 2 appears. We want to find how many sequences of rolls lead to a 2 appearing specifically on the kth roll.

2. **Rolls before the kth roll**: For the first \( k-1 \) rolls, we must not roll a 2. The possible outcomes for each of these rolls are 1, 3, 4, 5, or 6 (5 options).

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