Answer:
1/12
Step-by-step explanation:
<u>Needed information</u>
![\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}](https://tex.z-dn.net/?f=%5Csf%20Probability%5C%3Aof%5C%3Aan%5C%3Aevent%5C%3Aoccurring%20%3D%20%5Cdfrac%7BNumber%5C%3Aof%5C%3Aways%5C%3Ait%5C%3Acan%5C%3Aoccur%7D%7BTotal%5C%3Anumber%5C%3Aof%5C%3Apossible%5C%3Aoutcomes%7D)
The sum of the probabilities of all outcomes must equal 1
<u>Solution</u>
We are told that the probability that the counter is <em>not</em> black is 3/4.
As the sum of the probabilities of all outcomes <u>must equal 1</u>, we can work out the probability that the counter <em>is </em>black by subtracting 3/4 from 1:
![\sf P(counter\:not\:black)=\dfrac34](https://tex.z-dn.net/?f=%5Csf%20P%28counter%5C%3Anot%5C%3Ablack%29%3D%5Cdfrac34)
![\implies \sf P(counter\:black)=1-\dfrac34=\dfrac14](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%20P%28counter%5C%3Ablack%29%3D1-%5Cdfrac34%3D%5Cdfrac14)
We are told that the probability that the counter is <em>not </em>white is 2/3.
As the sum of the probabilities of all outcomes <u>must equal 1</u>, we can work out the probability that the counter <em>is </em>white by subtracting 2/3 from 1:
![\sf P(counter\:not\:white)=\dfrac23](https://tex.z-dn.net/?f=%5Csf%20P%28counter%5C%3Anot%5C%3Awhite%29%3D%5Cdfrac23)
![\implies \sf P(counter\:white)=1-\dfrac23=\dfrac13](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%20P%28counter%5C%3Awhite%29%3D1-%5Cdfrac23%3D%5Cdfrac13)
We are told that there are black, white and grey counters in the bag. We also know that the sum of the probabilities of all outcomes must equal 1. Therefore, we can work out the probability the counter is grey by subtracting the probability the counter is black and the probability the counter is white from 1:
![\begin{aligned}\sf P(counter\:grey) & = \sf1-P(counter\:black)-P(counter\:white)\\\\ & =\sf 1-\dfrac14-\dfrac13\\\\ & = \sf \dfrac{12}{12}-\dfrac{3}{12}-\dfrac{4}{12}\\\\ & = \sf \dfrac{12-3-4}{12}\\\\ & = \sf \dfrac{5}{12}\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Csf%20P%28counter%5C%3Agrey%29%20%26%20%3D%20%5Csf1-P%28counter%5C%3Ablack%29-P%28counter%5C%3Awhite%29%5C%5C%5C%5C%20%26%20%3D%5Csf%201-%5Cdfrac14-%5Cdfrac13%5C%5C%5C%5C%20%26%20%3D%20%5Csf%20%5Cdfrac%7B12%7D%7B12%7D-%5Cdfrac%7B3%7D%7B12%7D-%5Cdfrac%7B4%7D%7B12%7D%5C%5C%5C%5C%20%26%20%3D%20%5Csf%20%5Cdfrac%7B12-3-4%7D%7B12%7D%5C%5C%5C%5C%20%26%20%3D%20%5Csf%20%5Cdfrac%7B5%7D%7B12%7D%5Cend%7Baligned%7D)
Answer:
<em>x = -6</em>
Step-by-step explanation:
<u>Equations</u>
Solve the equation:
x + 6 = -x - 6
We must find the value of x that makes the identity above true.
Let's join all the variables on the left side and the numbers on the right side.
Adding x:
x + 6 + x = -x - 6 + x
The variables cancel out on the right side:
2x + 6 = -6
Subtracting 6:
2x + 6 - 6 = -6 -6
The 6 and -6 are canceled out:
2x = -12
Dividing by 2:
x = -12/2
x = -6
The answer is B. 97
3 x 27 + 2 x 8