A six-sided die is rolled three times. What is the probability of rolling a one on the first role, rolling a three on the second roll, and rolling a number greater than four on the third roll ?

Answer 1

The great thing about this question is that all three of those rolls are Independent Scenarios.

The probability of the first roll does not effect the outcome of the second or third roll!

1. 1/6 ( we want a 1, and there are 6 options.)
2. 1/6 ( We want a 3, and there are 6 options
3. 2/6 ( We want a 5 or 6, and there are 6 options)
4. Now if you want the probability of all that happening in a row, simply take the fractions and multiply them together. Giving you 2/216 or 1/108. Not very good odds....

Answer 2

The chance one gets a 1 on the first roll is 1/6. The chance of getting a 3 on the second roll is also 1/6. The chance of getting a number greater than 4 (5 or 6) is 2/6, or 1/3. These are all independent events and there is no double counting, so multiply and get 1/108.