Question

a weighted die has probability 0.102 of landing on a 6. if you roll the die until you get a 6 for the first time, what is the expected number of rolls it will take? round to the nearest integer.

Answer 1

To find the expected number of rolls to get a 6 on a weighted die, we use the reciprocal of the probability of rolling a 6, which is 0.102. After calculating, the expected number of rolls is about 9.8039, which rounds to the nearest integer as 10.

Step-by-step explanation:

To calculate the expected number of rolls it takes to get a 6 on a weighted die with a probability of 0.102, we use the concept of the geometric distribution. The expected number of trials (rolls) until the first success (landing a 6) in a geometric distribution is given by the reciprocal of the success probability, which is 1/p. In this case, p is the probability of rolling a 6, which is 0.102.

The calculation is therefore:

1. Expected number of rolls = 1 / p = 1 / 0.102
2. 1 / 0.102 ≈ 9.8039
3. Rounding to the nearest integer, the expected number of rolls is 10.