Two number cubes are rolled. Both cubes are labelled 1 to 6.
The numbers rolled are added.
a)The sum is 12.
b)The sum is less than 4.
c)The sum is 7.
d)The sum is 2.
So what is the question?
it is easy to list all the possible ways to roll the desired sums.
Then you can answer any questions about them.
To find the answers to these questions, we can analyze all the possible outcomes by listing the numbers on the two cubes.
Considering that both cubes are labeled 1 to 6, there are 36 possible outcomes when they are rolled simultaneously.
a) Let's identify the outcomes where the sum is 12. These are (6,6) and (6,6), so there are two possible outcomes out of 36.
b) The sum being less than 4 can only be achieved if both numbers rolled are 1. There is only one possible outcome where the sum is less than 4, which is (1,1).
c) Let's identify the outcomes where the sum is 7. These can be (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). Therefore, there are six possible outcomes out of 36.
d) The sum being 2 can only be achieved if both numbers rolled are 1. There is only one possible outcome where the sum is 2, which is (1,1).
In summary:
a) The probability of the sum being 12 is 2/36 or 1/18.
b) The probability of the sum being less than 4 is 1/36.
c) The probability of the sum being 7 is 6/36 or 1/6.
d) The probability of the sum being 2 is 1/36.