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
tresset_1 [31]
3 years ago
13

g A population is infected with a certain infectious disease. It is known that 95% of the population has not contracted the dise

ase. A test for this disease is 98% accurate (i.e., a person who has contracted the disease tests positive 98% of the time) and has a 1% false negative rate (i.e., a person without the disease has 1% positive rate). Find the probability that a random selected person from does not have the infection if he or she has tested positive. Briefly explain why you are or are not surprised by your result.
Mathematics
1 answer:
trasher [3.6K]3 years ago
7 0

Answer:

There is approximately 17% chance of a person not having a disease if he or she has tested positive.

Step-by-step explanation:

Denote the events as follows:

<em>D</em> = a person has contracted the disease.

+ = a person tests positive

- = a person tests negative

The information provided is:

P(D^{c})=0.95\\P(+|D) = 0.98\\P(+|D^{c})=0.01

Compute the missing probabilities as follows:

P(D) = 1- P(D^{c})=1-0.95=0.05\\\\P(-|D)=1-P(+|D)=1-0.98=0.02\\\\P(-|D^{c})=1-P(+|D^{c})=1-0.01=0.99

The Bayes' theorem states that the conditional probability of an event, say <em>A</em> provided that another event <em>B</em> has already occurred is:

P(A|B)=\frac{P(B|A)P(A)}{P(B|A)P(A)+P(B|A^{c})P(A^{c})}

Compute the probability that a random selected person does not have the infection if he or she has tested positive as follows:

P(D^{c}|+)=\frac{P(+|D^{c})P(D^{c})}{P(+|D^{c})P(D^{c})+P(+|D)P(D)}

              =\frac{(0.01\times 0.95)}{(0.01\times 0.95)+(0.98\times 0.05)}\\\\=\frac{0.0095}{0.0095+0.0475}\\\\=0.1666667\\\\\approx 0.1667

So, there is approximately 17% chance of a person not having a disease if he or she has tested positive.

As the false negative rate of the test is 1%, this probability is not unusual considering the huge number of test done.

You might be interested in
The teacher buys a pack of notebooks for give his students the ratio of the gold notebooks to red notebooks is represented in th
katovenus [111]

Answer-

              ~The answer is 40 gold notebooks~

                               (Thank me later~)

7 0
3 years ago
Read 2 more answers
Lastima Nelson, Inc. is recruiting a new Chief Financial Officer (CFO). The recruiting budget is $44,000. Lastima has spent $10,
Musya8 [376]
The budget is $44000

Total spent so far is $10000 + $8500 = $18500

The amount left to spend = 44000 - 18500 = $25500

$25500 is the maximum 6% commission that Lastima Nelson Inc. can spend and stays within the budget

Let the maximum price of the home be x
This value of x will be the 100% before the 6% commission is calculated of it.

6% of x is 25500
1% of x is 25500 ÷ 6 = $4250
100% of x is 4250 × 100 = $425,000

So, the maximum value of the home is $425,000
5 0
3 years ago
Find the value of 5x - 2y+ 3z when x = 7 , y = 11 and z = -1
Oksanka [162]
By replacing you get:

5*7-2*11+3*(-1) = 35-22-3= 10

so the answer is 10.

If you like my answers, feel free to follow me and ask me more maths problems. :)
7 0
3 years ago
Read 2 more answers
MATH 15 POINTS, HELP
7nadin3 [17]
Statement 3: tri egc = tri egb
statement 4: tri ebc is equilateral.
reason 5: equilateral triangles have equal angles
4 0
3 years ago
M || n, find the value of x.
yuradex [85]

Step-by-step explanation:

please mark me as brainlest

7 0
1 year ago
Other questions:
  • 320% as a fraction or mixed number in simplest form
    15·1 answer
  • I need help with this question i cant find the answer
    6·1 answer
  • What would be the future value of a savings account started with $675, earning 9 percent (compounded annually) after 7 years? (?
    15·1 answer
  • Solve 4x+2=12 for using the change of base formula logby=logy over logb
    9·2 answers
  • How many 3 digit palindromes are divisible by 9?
    11·1 answer
  • Describe the transformation f(x) = 2x + 1 -&gt; g(x) = -8(x + 4) - 1
    10·1 answer
  • What are the coordinates (x, y) at which the graphs of 2x + 3y = 12 and 2x - y = 4 intersect?
    11·2 answers
  • Electric &amp; energy energy answer sheet
    7·1 answer
  • An education researcher is interested in comparing the learning outcomes of students who are taught a lesson using five differen
    13·1 answer
  • Following decimals into words 15.06​
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!