Answer:
Explanation:
You can find the theoretical probability of the event "the sum of the numbers is at least 4".
The theoretical probability is:
- number of positive outcomes / number of possible outcomes.
<u>1. Number of positive outcomes.</u>
The number of positive outcomes is the amount of ways for which the sum of the numbers is at least 4.
Those are:
- Sum = 4: (1,3); (2,2), (3,1) → 3 ways
- Sum = 5: (1,4), (2,3), (3,2), (4,1) → 4 ways
- Sum = 6: (1,5), (2, 4), (3, 3), (4, 2), (5,1) → 5 ways
- Sum = 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) → 6 ways
- Sum = 8: (2,6), (3,5), (4,4), (3,5), (2,6) → 5 ways
- Sum = 9: (3,6), (4,5), (5,4), (6,3) → 4 ways
- Sum = 10: (4,6), (5,5), (6,4) → 3 ways
- Sum = 11: (5, 6), (6,5) → 2 ways
Thus, the total number of ways to have a sum of at least 4 is: 3 + 4 + 5 + 6 + 5 + 4 + 3 + 2 + 1 = 33.
<u>2. Number of possible outcomes</u>
The total number of possible outcomes is found by multiplying the ways each die can be rolled, this is: 6 × 6 = 36.
<u>3. Probability</u>
Then, the searched probability is 33/36 = 11/12 ≈ 0.92
Is there more to this question?
Step-by-step explanation:
Let the number be x, then
15 less than a product of 2 and a number
Answer:
2
+
1
1
+
3
0
Step-by-step explanation:
(
+
5
)
(
+
6
)
{\color{#c92786}{(x+5)(x+6)}}
(x+5)(x+6)
(
+
6
)
+
5
(
+
6
)
I would plug in each of the solutions to every equation and see which one works. This is probably easier than solving for x, y, and z. But let me know if you would like me to run through the steps!
First choice: using the first equation, -3(-3)-4(4)+6=-19 not -1 as listed. False.
Second choice: using the first equation, -3(4)-4(-3)+(-1)=-1 ; using the second equation, 2(4)+(-3)-(-1)=6 not -8 as listed. False.
Third choice: using the first equation, -3(-3)-4(4)+8=-17 not -1 as listed. False.
Fourth choice: using the first equation, -3(3)-4(-4)+-(-6)=-1 ; using the second equation,
2(3)+(-4)-(-6)=8 ; using the third equation, 3+8(-4)-(-6)=23
So the answer should be the fourth choice. Hope this helps! :)
