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) (6,4) (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)5/18
D)1/3
I don't understand how to solve this question please help!
How many sums are greater than 5?
6 can happen in 5 ways: (1,5),(2,4),(3,3),(4,2),(5,1)
Count the ways for 7,8,9,10,11,12
P(sum > 5) is (#ways to get a sum > 5)/36
To find the probability of getting a sum greater than 5 when rolling two number cubes, you need to count the number of outcomes where the sum is greater than 5 and divide it by the total number of possible outcomes.
Let's count the number of outcomes where the sum is greater than 5:
(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)
There are 21 outcomes where the sum is greater than 5.
Now, let's count the total number of possible outcomes:
Since there are 6 numbers on each number cube and two number cubes are rolled, the total number of outcomes is 6 * 6 = 36.
Finally, we can find the probability by dividing the number of successful outcomes (sum greater than 5) by the total number of outcomes: 21/36 = 7/12.
So, the correct answer is not listed among the given choices.
To find the probability that the sum of the two numbers rolled is greater than 5, we need to count the number of outcomes where the sum is greater than 5 and divide it by the total number of possible outcomes.
Let's start by listing all the outcomes where the sum is greater than 5:
(2,4), (2,5), (2,6)
(3,3), (3,4), (3,5), (3,6)
(4,2), (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)
Counting these outcomes, there are 22 favorable outcomes.
Next, let's find the total number of possible outcomes. In this case, it's the number of cells in the table, which is 6 rows multiplied by 6 columns, giving us 36 total outcomes.
Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of outcomes:
P(sum is greater than 5) = favorable outcomes / total outcomes = 22 / 36 = 11 / 18
So the answer is not among the given options.