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:
x = 18/5
Step-by-step explanation:
-5/6 x=-3
Multiply each side by -6/5
-6/5 *-5/6 x=-3*-6/5
x = 18/5
X = 180 -30
x = 150
-------------------------------
Answer:
Random sample
Step-by-step explanation:
It's a random sample because she did not pick the students 1 by 1, she just chose random students from a list