The sample space for a roll of two number cubes is shown in the table.
(1,1)|(1,2)|(1,3)|(1,4)|(1,5),(1,6)
(2,1)|(2,2)|(2,3)|(2,4)|(2,5)|(2,6)
(3,1)|(3,2)|(3,3)|(3,4)|(3,5)|(3,6)
(4,1)|(4,2)|(4,3)|(4,4)|(4,5)|(4,6)
(5,1)|(5,2)|(5,3)|(5,4)|(5,5)|(5,6)
(6,1)|(6,2)|(6,3)|(6,5)|(6,5)|(6,6)
The two numbers rolled can be added to get a sum. Find P(sum is greater than 5).
A. 5/6 ***
B. 13/18
C. 2/3
D. 1/2
correct
To find the probability that the sum of the two numbers rolled is greater than 5, we need to count the number of favorable outcomes (where the sum is greater than 5) and the total number of possible outcomes.
Let's go through the process step by step:
Step 1: Identify the favorable outcomes.
In this case, the sum of the two numbers will be greater than 5 if any of the following combinations occur:
- (1,6), (2,5), (2,6), (3,4), (3,5), (3,6), (4,3), (4,4), (4,5), (4,6), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)
Step 2: Count the number of favorable outcomes.
By counting the number of combinations listed above, we find that there are a total of 21 favorable outcomes.
Step 3: Count the total number of possible outcomes.
Looking at the sample space table, we can see that there are 36 possible outcomes.
Step 4: Calculate the probability.
To find the probability, we divide the number of favorable outcomes by the total number of possible outcomes:
P(sum is greater than 5) = favorable outcomes / total outcomes = 21 / 36 = 7 / 12
So, the correct answer is not listed among the given options.