A pair of dice is cast. What is the probability that the sum of the numbers landing upwards is 8 if it is known that the two numbers are different?
to get an 8, with no 44
that would leave 62 53 35 and 26
there are 4 of those
prob of 8 with different numbers = 4/36 = 1/9
To find the probability that the sum of the numbers landing upwards on a pair of dice is 8, given that the two numbers are different, we need to determine the total number of possible outcomes where the sum is 8 and the two numbers are different, and divide it by the total number of outcomes where the two numbers are different.
First, let's determine the total number of outcomes where the two numbers are different.
When rolling a pair of dice, each die has 6 possible outcomes. So, the total number of outcomes for both dice is 6 multiplied by 6, which equals 36.
Now, let's find the number of outcomes where the sum of the numbers landing upwards is 8 and the two numbers are different.
There are several ways to get a sum of 8 on a pair of dice: (2,6), (3,5), (4,4), (5,3), and (6,2).
Out of these possibilities, we need to exclude (4,4) since the question specifies that the two numbers must be different.
Therefore, there are a total of 4 possible outcomes where the sum is 8 and the two numbers are different.
Now, to find the probability, we divide the number of favorable outcomes (4) by the total number of possible outcomes (36):
Probability = Number of favorable outcomes / Total number of possible outcomes
= 4 / 36
= 1 / 9
So, the probability that the sum of the numbers landing upwards on a pair of dice is 8, given that the two numbers are different, is 1/9.