Answer:
![P(disease/positivetest) = 0.36116](https://tex.z-dn.net/?f=P%28disease%2Fpositivetest%29%20%3D%200.36116)
Step-by-step explanation:
This is a conditional probability exercise.
Let's name the events :
I : ''A person is infected''
NI : ''A person is not infected''
PT : ''The test is positive''
NT : ''The test is negative''
The conditional probability equation is :
Given two events A and B :
P(A/B) = P(A ∩ B) / P(B)
![P(B) >0](https://tex.z-dn.net/?f=P%28B%29%20%3E0)
P(A/B) is the probability of the event A given that the event B happened
P(A ∩ B) is the probability of the event (A ∩ B)
(A ∩ B) is the event where A and B happened at the same time
In the exercise :
![P(I)=0.025](https://tex.z-dn.net/?f=P%28I%29%3D0.025)
![P(NI)= 1-P(I)=1-0.025=0.975\\P(NI)=0.975](https://tex.z-dn.net/?f=P%28NI%29%3D%201-P%28I%29%3D1-0.025%3D0.975%5C%5CP%28NI%29%3D0.975)
![P(PT/I)=0.904\\P(PT/NI)=0.041](https://tex.z-dn.net/?f=P%28PT%2FI%29%3D0.904%5C%5CP%28PT%2FNI%29%3D0.041)
We are looking for P(I/PT) :
P(I/PT)=P(I∩ PT)/ P(PT)
![P(PT/I)=0.904](https://tex.z-dn.net/?f=P%28PT%2FI%29%3D0.904)
P(PT/I)=P(PT∩ I)/P(I)
0.904=P(PT∩ I)/0.025
P(PT∩ I)=0.904 x 0.025
P(PT∩ I) = 0.0226
P(PT/NI)=0.041
P(PT/NI)=P(PT∩ NI)/P(NI)
0.041=P(PT∩ NI)/0.975
P(PT∩ NI) = 0.041 x 0.975
P(PT∩ NI) = 0.039975
P(PT) = P(PT∩ I)+P(PT∩ NI)
P(PT)= 0.0226 + 0.039975
P(PT) = 0.062575
P(I/PT) = P(PT∩I)/P(PT)
![P(I/PT)=\frac{0.0226}{0.062575} \\P(I/PT)=0.36116](https://tex.z-dn.net/?f=P%28I%2FPT%29%3D%5Cfrac%7B0.0226%7D%7B0.062575%7D%20%5C%5CP%28I%2FPT%29%3D0.36116)
Answer:
A machine has 12 identical components which function independently. The probability that a component will fail is 0.2. The machine will stop working if more than three components fail. Find the probability that the machine will stop working. A) 0.073 B) 0.795 C) 0.867 D)0.205
Answer:
25 x 4 = 100
8 x 4 = 32 %
Step-by-step explanation:
Answer:
D)
Step-by-step explanation:
The answer is B: 4.5 cm, 7.5 cm
Here's why: 7.5 is 3 cm more than 4.5, and when added together, 7.5 + 7.5 + 4.5 + 4.5 = 24.