1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Vedmedyk [2.9K]
3 years ago
13

A certain virus infects one in every 300 people. A test used to detect the virus in a person is positive 90​% of the time when t

he person has the virus and ​15% of the time when the person does not have the virus.​ (This 15​% result is called a false positive​.) Let A be the event​ "the person is​ infected" and B be the event​ "the person tests​ positive." ​(a) Using​ Bayes' Theorem, when a person tests​ positive, determine the probability that the person is infected. ​(b) Using​ Bayes' Theorem, when a person tests​ negative, determine the probability that the person is not infected.
Mathematics
1 answer:
garik1379 [7]3 years ago
6 0

Answer:

a)  P[A/B] = 0,019     or     P[A/B] = 1,9 %

b)  P[A- /B-] = 0,9996       or    P[A- /B-] = 99,96 %

Step-by-step explanation:

Bayes Theorem :

P[A/B]  =  P(A) * P[B/A] / P(B)

The branches of events are as follows

Condition 1        real infection     1/300        and     not infection  299/300

Then

1.-    1/300      299/300

When the test is done   (virus present)  0,9 (+)    0,15 (-)

2.-   299/300

When the test is done  ( no virus )   0,15  (+)     0,85 (-)

Then:

P(A) = event person infected          P(B)  =  person test positive

a) P[A/B]  = P(A) * P[B/A] / P(B)

where   P(A)  = 1/300  =   0,0033   P[B/A] = 0,9    

Then P(A) * P[B/A] =  0,0033*0,9  =  0,00297

P(B)   is    ( 1/300 )*0,9  +  (299/300)*0,15

P(B) = 0,0033*0,9 + 0,9966*0,15    ⇒  P(B) = 0,1524

Finally

P[A/B] =  0,00297 /0,1524

P[A/B] = 0,019     or     P[A/B] = 1,9 %

b) Following sames steps:

P[A- /B-] = (299/300) * 0,85  / (299/300) * 0,85 + (1/300 * 0,1)

P[A- /B-] = 0,8471 /0,8474

P[A- /B-] = 0,9996       or    P[A- /B-] = 99,96 %

You might be interested in
Two similar triangular prisms have volumes of 27 square meters and 64 square meters.
Inessa [10]

Answer:

9/16

Step-by-step explanation:

First we need to know that the dimensions ratio, the surface area ratio and the volume ratio have the following relation:

volume ratio = dimension ratio ^3

surface area ratio = dimension ratio ^2

The volume ratio between small prism and the large prism is 27 / 64.

To find the dimensions ratio, we need to take the cubic root of the volume scale:

dimension ratio = 3√(27/64) = 3/4

Now, to find the surface area ratio, we just need to make the square of the dimension ratio:

surface area ratio = (3/4)^2 = 9/16

8 0
2 years ago
What perfect square that is between 1 and 100 has 27 as one of its factors?
astra-53 [7]

Answer:

81

Step-by-step explanation:

Its a perfect square and 27*3=81

6 0
3 years ago
What is the interquartile range of the data set? {18, 17, 10, 25, 20, 20, 30, 18, 18, 30, 25} Enter the answer in the box. PLEAS
sasho [114]
The interquartile is 21
7 0
3 years ago
Read 2 more answers
I will give brainliest to person who answers correctly!
Crank

Answer:

41 is the answer .......

4 0
3 years ago
7. The points P(2, -3), Q(3, -2) and R(8, z) are
Hatshy [7]

Answer:

z = 3

Step-by-step explanation:

Since the points are collinear then the slopes between the points are equal.

Calculate the slope m using the slope formula

m = \frac{y_{2}-y_{1}  }{x_{2}-x_{1}  }

with (x₁, y₁ ) = P (2, - 3) and (x₂, y₂ ) = Q (3, - 2)

m = \frac{-2+3}{3-2} = 1

Repeat with

(x₁, y₁ ) = Q (3, - 2) and (x₂, y₂ ) = R (8, z )

m = \frac{z+2}{8-3} = \frac{z+2}{5} , then

\frac{z+2}{5} = 1 ( multiply both sides by 5 )

z + 2 = 5 ( subtract 2 from both sides )

z = 3

4 0
2 years ago
Other questions:
  • What is 21/56 simplified
    10·2 answers
  • Type the correct answer in each box. Spell all words correctly, and use numerals instead of words for numbers. If necessary, use
    8·2 answers
  • CAN SOMEONE PLS HELP ME ON THIS ONE.....
    15·2 answers
  • I have two congruent sides. I also have two congruent angles that measure 45 degree each. I am a
    15·1 answer
  • On a 16 scale drawing of a bike, one part is 3 inches long. How long will the actual bike part be?
    12·2 answers
  • Name 12 different rays
    12·1 answer
  • The results of a two-factor analysis of variance produce df = 2, 36 for the F-ratio for factor A and df = 2, 36 for the F-ratio
    11·1 answer
  • Que es el concepto de funcion?
    7·1 answer
  • Pls I need help<br> Solve <br> x-4=⅓(6x-54)
    6·2 answers
  • Please help!!! 20 points
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!