Answer:
The probability of the defendant is innocent given the defendant is convicted is P=0.006.
Step-by-step explanation:
Being:
G: guilty, I:innocent, C: convicted, A: acquitted.
We need to calculate P(I|C).
Being innocent, given convicted, is equal to the probability of being innocent and convicted divided by the probability of being convicted (innocent or guilty)
![P(I|C)=\frac{P(I\&C)}{P(C)}](https://tex.z-dn.net/?f=P%28I%7CC%29%3D%5Cfrac%7BP%28I%5C%26C%29%7D%7BP%28C%29%7D)
The probability of being innocent and convicted is
![P(I\&C)=P(C|I)*P(I)=0.05*0.1=0.005](https://tex.z-dn.net/?f=P%28I%5C%26C%29%3DP%28C%7CI%29%2AP%28I%29%3D0.05%2A0.1%3D0.005)
The probability of being convicted is equal to the sum of P(I&C) and P(G&C)
![P(C)=P(I\&C)+P(I\&C)=P(C|I)*P(I)+P(C|G)*P(G)\\\\P(C)=0.005+0.95*0.90=0.005+0.855=0.86](https://tex.z-dn.net/?f=P%28C%29%3DP%28I%5C%26C%29%2BP%28I%5C%26C%29%3DP%28C%7CI%29%2AP%28I%29%2BP%28C%7CG%29%2AP%28G%29%5C%5C%5C%5CP%28C%29%3D0.005%2B0.95%2A0.90%3D0.005%2B0.855%3D0.86)
Then,
![P(I|C)=\frac{P(I\&C)}{P(C)}=\frac{0.005}{0.86}= 0.006](https://tex.z-dn.net/?f=P%28I%7CC%29%3D%5Cfrac%7BP%28I%5C%26C%29%7D%7BP%28C%29%7D%3D%5Cfrac%7B0.005%7D%7B0.86%7D%3D%200.006)
Answer:
A. ..........
Step-by-step explanation:
Answer:
z = -12
Step-by-step explanation:
Rewritting the equations, we have:
x + y = xy (eq1)
2x + 2z = xz (eq2)
3y + 3z = yz (eq3)
From the first equation:
x = y/(y-1) (eq4)
From the third equation:
y = 3z/(z - 3) (eq5)
Using the value of y from (eq5) in (eq4), we have:
x = [3z/(z - 3)] / [3z/(z - 3) - 1]
x = [3z/(z - 3)] / [(3z - z + 3)/(z - 3)]
x = 3z / (2z + 3) (eq6)
Using the value of x from (eq6) in (eq2), we have:
6z / (2z + 3) + 2z = (3z / (2z + 3))*z
(6z + 4z^2 + 6z) / (2z + 3) = 3z^2 / (2z + 3)
12z + 4z^2 = 3z^2
z^2 = -12z
z = -12
Pretty sure it’s C sorry if wrong