Using conditional probability, it is found that the probability a person who tests positive actually has the disease is 0.087 = 8.7%.
<h3>What is Conditional Probability?</h3>
Conditional probability is the probability of one event happening, considering a previous event. The formula is:
![P(B|A) = \frac{P(A \cap B)}{P(A)}](https://tex.z-dn.net/?f=P%28B%7CA%29%20%3D%20%5Cfrac%7BP%28A%20%5Ccap%20B%29%7D%7BP%28A%29%7D)
In which:
- P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
- P(A) is the probability of A happening.
For this problem, the events are given as follows:
- Event B: Person has the disease.
The percentages associated with a positive test is:
- 95% of 0.5%(person has the disease).
- 5% of 99.5%(person does not have the disease).
Hence:
P(A) = 0.95 x 0.005 + 0.05 x 0.995 = 0.0545.
The probability of both a positive test and having the disease is:
![P(A \cap B) = 0.95 \times 0.005 = 0.00475](https://tex.z-dn.net/?f=P%28A%20%5Ccap%20B%29%20%3D%200.95%20%5Ctimes%200.005%20%3D%200.00475)
Hence the conditional probability is:
P(B|A) = 0.00475/0.0545 = 0.087.
The probability a person who tests positive actually has the disease is 0.087 = 8.7%.
More can be learned about conditional probability at brainly.com/question/14398287
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Answer:
SA=736ft²
Step-by-step explanation:
First I like to start with the triangles
![a =2 \frac{1}{2} bh \\](https://tex.z-dn.net/?f=a%20%3D2%20%5Cfrac%7B1%7D%7B2%7D%20bh%20%5C%5C%20)
The reason why we would multiply the triangle area by two is because where finding the area of the triangle in the Back and in the front
![a = 2 \frac{1}{2} (12 \times 8) = 96](https://tex.z-dn.net/?f=a%20%3D%202%20%5Cfrac%7B1%7D%7B2%7D%20%2812%20%5Ctimes%208%29%20%3D%2096)
then we go to the rectangles of the left and right
![a = 2bh](https://tex.z-dn.net/?f=a%20%3D%202bh)
![a = 2(20 \times 10) = 400](https://tex.z-dn.net/?f=a%20%3D%202%2820%20%5Ctimes%2010%29%20%3D%20400)
again because the numbers for the base and height of the two rectangles are the same we are going to times by two.
Then we going to find the area for the base of the triangular prism, which would be the bottom rectangle
![a = bh](https://tex.z-dn.net/?f=a%20%3D%20bh)
there are no same shapes with the same base and height so where not going to multiply by two
![a = 12 \times 20 = 240](https://tex.z-dn.net/?f=a%20%3D%2012%20%5Ctimes%2020%20%3D%20240)
now we add all the area that we found up
![400 + 96 + 240 = 736](https://tex.z-dn.net/?f=400%20%2B%2096%20%20%2B%20240%20%3D%20736)
now we have 736ft and since where finding SA we square it
SA=736ft²
You need to know what the distance jesse traveled is and then the number of gallons of gas she has then you plug it it.
distance equals 15 times the amount of gas in gallons
d=15g
The value of k in <span>
1/2 k+6=4k-8</span>
is 4
Answer:
15 nickels and 8 dimes
Step-by-step explanation:
Create a system of equations where d is the number of dimes and n is the number of nickels:
0.1d + 0.05n = 1.55
n = d + 7
Solve with substitution by plugging in d + 7 as n:
0.1d + 0.05(d + 7) = 1.55
0.1d + 0.05d + 0.35= 1.55
0.15d + 0.35 = 1.55
0.15d= 1.2
d = 8
Plug in 8 as d to find n:
n = d + 7
n = 8 + 7
n = 15
So, there are 15 nickels and 8 dimes