Question

Calculate the probability of rolling the first 1 on the (k+1)-th toss of an n-sided die with sides labeled 1,2,...,n.

i. (1 - 1/n) * n^k
ii. (1 - 1/n)^k * 1/n
iii. (1 - 1/n)^k * n^k
iv. (1 - 1/n) * 1/n

Answer 1

The probability of rolling the first 1 on the (k+1)-th toss of an n-sided die can be calculated using the formula (1 - 1/n)^k * 1/n. Hence, ii) is correct.

Step-by-step explanation:

The probability of rolling the first 1 on the (k+1)-th toss of an n-sided die can be calculated using the formula (1 - 1/n)^k * 1/n.

Here's a step-by-step explanation:

1. The probability of not rolling a 1 on a single toss is 1 - 1/n, as there are n-1 outcomes that are not 1.
2. Since each toss is independent, the probability of not rolling a 1 on the first k tosses is (1 - 1/n)^k.
3. Finally, the probability of rolling a 1 on the (k+1)-th toss is obtained by multiplying the probability of not rolling a 1 on the first k tosses by the probability of rolling a 1 on a single toss, which is 1/n.

Therefore, the correct answer is (1 - 1/n)^k * 1/n.