00:01
In this exercise, we have a pair of six -sided dice being rolled, and we are asked for some probabilities of certain outcomes for the pair of dice.
00:11
So here are the 36 different possible rows for a pair of dice.
00:18
For part a, we are asked for the probability that the sum is less than four.
00:32
So here we can use the frequentest approach to probability by finding the number of ways, or the number of outcomes, with the sum less than 4 divided by the total number of possible outcomes.
01:05
The number of outcomes with a sum less than 4 means that the sum must be 3 or less.
01:13
So that is these three dice rolls here.
01:17
Anything else has a sum of 4 or more.
01:21
So in the numerator we have 3 and in the denominator we have 36.
01:28
This gives us a probability of 1 over 12.
01:34
For b, we are asked for the probability that both dice have the same number...