SOLUTION: An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face v
Algebra.Com
Question 1194146: An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment.
Compute the probability of each of the following events:
Event A: the sum is greater than 8.
Event B: the sum is an even number.
round answer two demical points
P(A)=
P(B)=
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!
We'll start with P(A).
Let's say we have two dice, one red and the other blue
Each is labeled 1 through 6
The 36 possible dice sums are listed below
| + | 1 | 2 | 3 | 4 | 5 | 6 |
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| 6 | 7 | 8 | 9 | 10 | 11 | 12 |
Use that table to determine...- There are 4 ways to roll a 9
- There are 3 ways to roll a 10
- There are 2 ways to roll an 11
- There is 1 way to roll a 12
In all, there are 4+3+2+1 = 10 ways to get a sum that is larger than 8.
This is out of the 36 total outcomes
10/36 = (5*2)/(18*2) = 5/18 = 0.28 is the approximate value of P(A)
Event A happens roughly 28% of the time.
------------------------------------------------------------
Now onto calculating P(B)
Refer to the chart above- There is 1 way to roll a 2
- There are 3 ways to roll a 4
- There are 5 ways to roll a 6
- There are 5 ways to roll an 8
- There are 3 ways to roll a 10
- There is 1 way to roll a 12
Adding up those frequencies gets us 1+3+5+5+3+1 = 18
Then dividing that over the total 36 outcomes yields 18/36 = 1/2 = 0.50 which is the value of P(B).
This is to be expected since half of the numbers on the die are even, so the sum being even should happen half the time.
Side notes:
even + even = even
odd + even = odd
odd + odd = even
------------------------------------------------------------
Answers:
P(A) = 0.28
P(B) = 0.50
RELATED QUESTIONS
An ordinary (fair) die is a cube with the numbers
1
through
6
on the sides... (answered by solver91311)
An ordinary (fair) die is a cube with the numbers
1 through 6 on the sides (represented (answered by Edwin McCravy)
An ordinary (fair) die is a cube with the numbers
1
through
6
on the sides... (answered by Boreal)
An ordinary (fair) die is a cube with the numbers
1
through
6
on the sides... (answered by ikleyn)
An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (represented... (answered by stanbon)
An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (represented... (answered by Boreal)
An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (represented... (answered by ikleyn)
Die rolling
An ordinary (fair) die is a cube with the numbers through on the sides... (answered by edjones)
An ordinary (fair) die is a cube with the numbers through on the sides (represented by... (answered by Boreal)
An ordinary (fair) die is a cube with the numbers through on the sides (represented by... (answered by stanbon)