Question

Harvey has a fair eight-sided die that has a different number from 1 to 8 on each side. If he rolls the die twice, what is the probability that the second number rolled is greater than or equal to the first number? Express answer as a common fraction.

Answer 1

The probability that the second number rolled is greater than or equal to the first number when rolling a fair eight-sided die twice is 1/16.

Step-by-step explanation:

To find the probability that the second number rolled is greater than or equal to the first number when rolling a fair eight-sided die twice, we need to determine the favorable outcomes and the total number of possible outcomes.

There are 8 possible outcomes for the first roll and 8 possible outcomes for the second roll. However, since the die is fair and has different numbers on each side, the second roll can only be greater than or equal to the first roll for 4 of the outcomes.

Therefore, the probability is 4 favorable outcomes out of 64 total outcomes, which simplifies to a probability of B

Answer 2

It depends on what the first roll was

On the first roll, every number has a 1/8 chance to be rolled

On the second roll, a lower number on the first roll has a greater chance to have a higher number rolled or the same number the second time.

First roll is...
1 : probability to be out rolled or equal roll 8/8 or 1/1
2 : probability to be out rolled or equal roll 7/8
3 : probability to be out rolled or equal roll 6/8 or 3/4
4 : probability to be out rolled or equal roll 5/8
5 : probability to be out rolled or equal roll 4/8 or 1/2
6 : probability to be out rolled or equal roll 3/8
7 : probability to be out rolled or equal roll 2/8 or 1/4
8 : probability to be out rolled or equal roll 1/8

Hope this helps :)