Suppose that one person in 10,000 people has a rare genetic disease. There is an excellent test for the disease; 99.9% of people with the disease test positive and only 0.02% who do not have the disease test positive.
What is the probability that someone who tests positive does not have the genetic disease?
What is the probability that someone who tests negative has the disease?

Part a: The probability that someone tests positive and does not have the disease is given as P(F'|E) is 0.6667

Part b: The probability that someone tests negative and  have the disease is given as P(F|E') is 0.000000103

Step-by-step explanation:

The event that the test is positive is  E and the patient has disease is  F

so

The probability of a person having disease is  P(F)=1/10000=0.0001

The probability of a person having disease and test positive is  P(E|F)=0.999

The probability of a person not having disease and testing positive is  P(E|F')=0.0002

Now by using complement rule, the value of people not having the disease is  P(F')=1-P(F)=1-0.0001=0.9999

Part a:

The probability that someone tests positive and does not have the disease is given as P(F'|E) by Bayes theorem is as

By substitution of the values

The probability that someone tests positive and does not have the disease is given as P(F'|E) is 0.6667

Part b

The probability that someone tests positive and does not have the disease is given as P(F|E') by Bayes theorem is as

The probabilities are calculated as

P(E'|F)=1-P(E|F)=1-0.999=0.001

P(E'|F')=1-P(E|F')=1-0.0002=0.9998

By substitution of the values

The probability that someone tests negative and have the disease is given as P(F|E') is 0.000000103

location: point 0

step-by-step explanation:

well, -8 to 10 on a number line is 18 spaces.

1/9 of 18 is 2.

so, 4/9 of 18 must be 8.

8 spaces from -8 (a) is 0.

so, 4/9 of the way from -8 to 10 is 0!

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240