So let's get k on one side:
2k = 2
Divide by 2:
k = 1
If you want to check your work:
1 + 1 = 3 - 1
2 = 2
Answer:
a) ![P(B/A) = P(B)](https://tex.z-dn.net/?f=P%28B%2FA%29%20%3D%20P%28B%29)
Step-by-step explanation:
<u><em>Step(i):-</em></u>
Given that A and B are independent events
P(A∩B) =P(A) P(B)
we will use the conditional probability
![P(A/B) = \frac{P(AnB)}{P(B)}](https://tex.z-dn.net/?f=P%28A%2FB%29%20%3D%20%5Cfrac%7BP%28AnB%29%7D%7BP%28B%29%7D)
or
<u></u>
<u> Step(ii):-</u>
Given that A and B are independent events
P(A∩B) =P(A) P(B)
<u></u>
![P(B/A) = \frac{P(A)P(B)}{P(A)} = P(B)](https://tex.z-dn.net/?f=P%28B%2FA%29%20%3D%20%5Cfrac%7BP%28A%29P%28B%29%7D%7BP%28A%29%7D%20%3D%20P%28B%29)
![P(B/A) = P(B)](https://tex.z-dn.net/?f=P%28B%2FA%29%20%3D%20P%28B%29)
X-y=3
x=3+y
3+y+2y=8
3y=5
y=5/3
x=4 and 2/3