When we roll one die, we have a 1 in 6 probability of getting any particular number on the die. When we roll a pair of dice, there are 36 different pairs that can be produced, yet only 11 actual distinct values. Explain how the probability associated with the roll of each individual die in the pair explains the higher variability in the total outcome of the roll of each pair. How do the concepts of permutations and combinations apply to this example

permutations and combination principles would have to be applied to determine the probability of a particular number showing up when a pair of dice is rolled ,while a single dice roll have a fixed frequency of every event ( 1,2,3,4,5,6,) hence probability of a number showing up is 1/6

Step-by-step explanation:

The probability of an event occurring depends on the sample space and the frequency of the event

The total outcomes of rolling a pair of fair dice would be = ( total outcome of single dice A * total outcome of single Dice B ) = 6 * 6 = 36. and this is because the Two dice are independent of each other. hence there is a higher variability in the determining the possibility of a particular number ( 1,2,3,4,5,6) showing up when a pair of dice is rolled due to the larger sample space. permutations and combination principles would have to be applied to determine the probability of a particular number showing up when a pair of dice is rolled ,while a single dice roll have a fixed frequency of every event ( 1,2,3,4,5,6,) hence probability of a number showing up is 1/6