<h3>
Answer: 1/8</h3>
In decimal form, 1/8 = 0.125 which converts to 12.5%
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Work Shown:
The 63 should be 6^3. There are 6 choices per slot, and 3 slots, so 6^3 = 216 different outcomes.
Here are all of the ways to add to 11 if we had 3 dice
- sum = 1+4+6 = 11
- sum = 1+5+5 = 11
- sum = 1+6+4 = 11
- sum = 2+3+6 = 11
- sum = 2+4+5 = 11
- sum = 2+5+4 = 11
- sum = 2+6+3 = 11
- sum = 3+2+6 = 11
- sum = 3+3+5 = 11
- sum = 3+4+4 = 11
- sum = 3+5+3 = 11
- sum = 3+6+2 = 11
- sum = 4+1+6 = 11
- sum = 4+2+5 = 11
- sum = 4+3+4 = 11
- sum = 4+4+3 = 11
- sum = 4+5+2 = 11
- sum = 4+6+1 = 11
- sum = 5+1+5 = 11
- sum = 5+2+4 = 11
- sum = 5+3+3 = 11
- sum = 5+4+2 = 11
- sum = 5+5+1 = 11
- sum = 6+1+4 = 11
- sum = 6+2+3 = 11
- sum = 6+3+2 = 11
- sum = 6+4+1 = 11
There are 27 ways to add to 11 using 3 dice. This is out of 216 total outcomes of 3 dice being rolled.
So, 27/216 = (1*27)/(8*27) = 1/8 is the probability of getting 3 dice to add to 11.
Assuming that the inequality you were going for was a ≤, set both polynomials less than or equal to 0.
x - 3 ≤ 0
x + 5 ≤ 0
For the first equation add 3 to both sides of the inequality. For the second, subtract 5 from both sides.
x ≤ 3
x ≤ - 5
These would be your solutions I guess, however, if you want to expand upon that, your actual answer is (- ∞, - 5] because if you were to plot these two inequalities on a number line, that is where the overlap would occur.
the answer to your question there would be 12
