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SVETLANKA909090 [29]
3 years ago
7

Suppose 10000 people are given a medical test for a disease. About1% of all people have this condition. The test results have a

15% false positive rate and a 10% false negative rate. What percent of the people who tested positive actually have the disease?
Mathematics
1 answer:
Alina [70]3 years ago
3 0

Answer:

The percent of the people who tested positive actually have the disease is 38.64%.

Step-by-step explanation:

Denote the events as follows:

<em>X</em> = a person has the disease

<em>P</em> = the test result is positive

<em>N</em> = the test result is negative

Given:

P(X)=0.01\\P(P|X^{c})=0.15\\P(N|X)=0.10

Compute the value of P (P|X) as follows:

P(P|X)=1-P(P|X^{c})=1-0.15=0.85

Compute the probability of a positive test result as follows:

P(P)=P(P|X)P(X)+P(P|X^{c})P(X^{c})\\=(0.85\times0.10)+(0.15\times0.90)\\=0.22

Compute the probability of a person having the disease given that he/she was tested positive as follows:

P(X|P)=\frac{P(P|X)P(X)}{P(P)}=\frac{0.85\times0.10}{0.22} =0.3864

The percentage of people having the disease given that he/she was tested positive is, 0.3864 × 100 = 38.64%.

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2 years ago
Alex wants to fence in an area for a dog park. He has plotted three sides of the fenced area at the points E (1, 5), F (3, 5), a
hram777 [196]

Answer:

(1,1)

Step-by-step explanation:

Given: E, F, G, H denote the three coordinates of the area fenced

To find: coordinates of point H

Solution:

According to distance formula,

length of side joining points (x_1,y_1)\,,\,(x_2,y_2) is equal to \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

So,

EF=\sqrt{(3-1)^2+(5-5)^2}=2\,\,units\\FG=\sqrt{(6-3)^2+(1-5)^2}=\sqrt{9+16}=5\,\,units\\GH=\sqrt{(x-6)^2+(y-1)^2}\\EH=\sqrt{(x-1)^2+(y-5)^2}

Perimeter of a figure is the length of its outline.

EF+FG+GH+EH=16\\2+5+\sqrt{(x-6)^2+(y-1)^2}+\sqrt{(x-1)^2+(y-5)^2}=16\\\sqrt{(x-6)^2+(y-1)^2}+\sqrt{(x-1)^2+(y-5)^2}=16-2-5\\\sqrt{(x-6)^2+(y-1)^2}+\sqrt{(x-1)^2+(y-5)^2}=9

Put (x,y)=(1,1)

\sqrt{(1-6)^2+(1-1)^2}+\sqrt{(1-1)^2+(1-5)^2}=9\\\sqrt{25}+\sqrt{16}=9\\5+4=9\\9=9

This is true.

So, the point (1,1) satisfies the equation \sqrt{(x-6)^2+(y-1)^2}+\sqrt{(x-1)^2+(y-5)^2}=9

So, point H is (1,1).

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All triangle angles have 60 degree angles. What are the side lengths?
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3 0
3 years ago
Read 2 more answers
In RSM camp, there are four counselors for every fifty seven students and three teachers for every five counselors.
Ray Of Light [21]

Answer:

Students : Counselors : Teachers = 285: 20 : 12

Step-by-step explanation:

In the camp, the ratio of:

( C: S )  Counselors : Students   is  4   :  57

( T: C )  Teachers :   Counselors  is  3   :  5

To determine the ratio of   -  Students : Counselors : Teachers

Here given      -  C : S  = 4 : 57

Multiplying both sides by 5, we get

C: S  = 4 x 5  : 57 x 5  = 20 : 285

So, for every 20 counselors, there are 285 students      ...... (1)

Similarly, given   Teachers :   Counselors  is  3   :  5

Multiplying both sides by 4, we get

T  : C  = 3 x 4  : 5 x 4  = 12  : 20

So, for every 12  teachers, there are 20 Counselors      ...... (2)

Hence, in both equation 1 and 2 the number of counselors is same = 20 .

Hence, both the ratios acne be combined.

So we get C : S  = 20 : 285      and T : C  = 12: 20

Inverting the values

⇒  S : C  = 285 : 20         and C : T  = 20 : 12

or, S : C : T  = 285: 20 : 12

or, Students : Counselors : Teachers = 285: 20 : 12

Hence, for every 285 students there are 20 counselors and 12 teachers.

4 0
3 years ago
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