Ninety-two percent of the people who have a particular disease will have a positive result on a given
diagnostic test. Ninety-six percent of the people who do not have the disease will have a negative result on
this test. Suppose 5 percent of the population has the disease.
7. Draw a tree diagram to illustrate these probabilities.

8. What percent of the population would test positive for the disease?

9. If someone from the population tests positive, what is the probability that (s)he has the disease?

Answers

Answer 1

99.4% chance that you are healthy if you receive a negative test. 67.9% chance that you are sick if you receive a positive test.

How to calculate probability?

14% of population would test positive for the disease

Step 1. Give algebraic names to various events described:

Let the event A represent the event that the diagnostic test gives a positive resultthe event E1 represent the event that a person has the particular disease, and, the event E2= not E1 represent the event that a person does not have the particular disease.

Step-2: Model the given situation mathematically.

It is given that ninety percent of the people who have the disease will have a positive result on a given diagnostic test.In other words, the conditional probability of the event that the diagnostic test gives a positive result (A) given that the tested person has the disease (E1) is given to be 90% Thus, P(A/E1)=90%It is also given that ninety percent of the people who do not have the disease will have a negative result on a given diagnostic test.

In other words, the conditional probability of the event that the diagnostic test gives a negative result (not A), given that the tested person does not have the disease (E2 = not E1) is given to be 90%

Thus P(not A/E2)=90%

Further, it is given that five percent of the population has the disease. In other words, the event that a person has the disease (E1) has the probability of 5% Thus P(E1)=5%

It is needed to find what percent of that population would test positive for the disease.

Thus, the probability that a person will have a positive result when tested, P(A) is to be determined.

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Related Questions

what is the resultant displacement of 6m north 8m east and 10m north west?

Answers

The resultant displacement is approximately 13.071m north and 8m east.

To find the resultant displacement, we need to combine the given displacements in a vector-like manner.

Let's break down the displacements into their components and then add them up.

The first displacement is 6m north.

Since it is purely in the north direction, its components would be 6m in the north direction (along the y-axis) and 0m in the east direction (along the x-axis).

The second displacement is 8m east.

As it is purely in the east direction, its components would be 0m in the north direction and 8m in the east direction.

The third displacement is 10m northwest.

To find its components, we can split it into two perpendicular directions: north and west.

The northwest direction can be thought of as the combination of north and west, each with a magnitude of 10m.

Since they are perpendicular, we can use the Pythagorean theorem to find the components.

The north component would be 10m multiplied by the cosine of 45 degrees (45 degrees because northwest is halfway between north and west).

Similarly, the west component would be 10m multiplied by the sine of 45 degrees.

Calculating the components:

North component = 10m [tex]\times[/tex] cos(45°) = 10m [tex]\times[/tex] 0.7071 ≈ 7.071m

West component = 10m [tex]\times[/tex] sin(45°) = 10m [tex]\times[/tex] 0.7071 ≈ 7.071m

Now, let's add up the components:

North component: 6m (from the first displacement) + 7.071m (from the third displacement) = 13.071m north

East component: 8m (from the second displacement).

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The graph represents a relation where x represents the independent variable and y represents the dependent variable.

A coordinate plane with points at negative 4 comma 4, negative 2 comma 0, 0 comma negative 3, 3 comma 1, and 5 comma negative 2.

What is the domain of the relation?

{−4, −3, −2, 0, 1, 3, 4, 5}
{−4, −2, 0, 3, 5}
{−3, −2, 0, 1, 4}
{0, 3, 4, 5}

Answers

The domain of the relation of the graph representing a relation where x represents the independent variable and y represents the dependent variable is {−4, −2, 0, 3, 5}.

How to determine domain relation?

The domain of a relation is the set of all possible input values (independent variable) for which the relation is defined.

Looking at the given points, the x-coordinates are -4, -2, 0, 3, and 5. So, the possible input values are -4, -2, 0, 3, and 5.

Therefore, the domain of the relation is {−4, −2, 0, 3, 5}.

Hence, the correct option is {−4, −2, 0, 3, 5}.

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XZ.P Point P(-7, 2) is mapped onto P¹ (3, -11) by the reflection y=mx+c. find the values of the constants m and c.

Answers

The values of the constants m and c include the following:

m = -1.3

c = 7.1

What is the slope-intercept form?

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + c

Where:

m represent the slope or rate of change.x and y are the points.c represent the y-intercept or initial value.

Since the point P(-7, 2) is mapped onto P' (3, -11) by the reflection y = mx + c, we can write the following system of equations;

2 = -7m + c ...equation 1.

-11 = 3m + c ...equation 2.

By solving the system of equations simultaneously, we have:

2 = -7m - 3m - 11

11 + 2 = -10m

13 = -10m

m = -1.3

c = 7m + 2

c = 7(-1.3) + 2

c = -7.1

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The Nut Shack sells cashews for $6.80 per pound and Brazil nuts for $4.70 per pound. How much of
each type should be used to make a 37 pound mixture that sells for $5.78 per pound?
Round answers to the nearest pound.
pounds of cashews
pounds of Brazil nuts
> Next Question

Answers

Answer:

Step-by-step explanation:

$6.80 x 19 pounds = $129.2

$4.70 x 18 pounds = $84.6

+___________________

37 pounds = $213.8

$213.8 divided by 37 pounds = 5.77837......

= $5.78 per pound

Can someone pls explain

Answers

163. The distance between A(-5, 6) and B(5, -5) is: AB ≈ 14.9 units

164. Applying the Pythagorean theorem, we have: Diagonal ≈ 21.2 ft.

165. Marissa's final answer is wrong. It should be, c = √676 = 26 units.

166. Missing side = 29 ft.

What is the Pythagorean Theorem?

The Pythagorean theorem states that c² = a² + b², given that a and b are shorter legs and c is the hypotenuse or longest leg of the right triangle.

163. The distance between A(-5, 6) and B(5, -5):

AB = √[(5−(−5))² + (−5−6)²]

AB = √221

AB ≈ 14.9 units

164. Apply the Pythagorean theorem to find the diagonal:

Diagonal = √(15² + 15²) ≈ 21.2 ft.

165. The answer Marissa got is wrong. The final answer which is the square root of 676 is:

c = √676 = 26 units.

166. Missing side = √(20² + 21²) = 29 ft.

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Question 1b Identify the amount in this statement. 6 is 30% of 20. The amount = The solution is

Answers

The amount in this statement, 6 is 30% of 20 is 6.

The amount in the statement "6 is 30% of 20" is 6.

This statement means that if we take 30% of 20, we get 6.

In other words, the amount 6 is 30% of 20.

We can also verify this by calculating 30% of 20:

30% of 20

= (30/100) × 20

= 0.3 × 20

= 6

Hence, the amount in this statement is 6.

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Need help asap, please and thank you

Answers

If the population in the year 2007 is 111.3 million, then the population in the year 2044 will be 148.37 million.

In order to find the population in the year 2044, we use the population growth formula; which is : P = P₀ × (1 + r)ⁿ;

where P = future population, P₀ = initial population, r = annual growth rate, and n = number of years;

Substituting the values,

We get;

⇒ P = (111.3 million) × (1 + 0.0078)²⁰⁴⁴⁻²⁰⁰⁷;

Simplifying this expression,

We get;

⇒ P = (111.3 million) × (1.0078)³⁷;

⇒ P ≈ 148.37 million;

Therefore, the population in the year 2044 is estimated to be approximately 148.37 million.

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someone please answer this its confusing me

Answers

24. opposite sides of a parallelogram are always congruent

the line AB will be congruent to line DC so 8t + 7 = 9t - 2 which gives you t = 9

line AD will also be congruent to line BC so 4s + 1 = 2s + 25 which gives you s = 12

If ARSU-AVST, then the triangles are
similar by:

Answers

Answer:

AA sim post

Step-by-step explanation:

They DO have equal (similar) angles.....but they do not have equal sides

Carlos is a door to door vacuum salesman. His weekly salary, S, is $400 plus $35 for each vacuum he sells.

This can be written as S = 400+35v , where v is the number of vacuums sold.

If Carlos earns $1590 for a week's work, how many vacuums did he sell?

Answers

Answer:

Step-by-step explanation:

1. Plug in the week's salary into the formula

S=400+35v

1590=400+35v

2. Solve for v.

1590=400+35v

Subract 400 from both sides. Since the opposite of addition is subraction, soing this cancels out the 400.

1190=35v

Divide each side by 35. Since the opposite of multiplication (35v = 35 times v) is division, this will cancel out the 35.

34=v

HELP PLEASE PHOTO INCLUDED

Answers

Answer:

Eat that cookie and you will not regret about it

Help My Daughter we not understanding?

Answers

Representation of a number in three different ways:

133: [12 tens and 13 ones], [13 tens and 3 ones], [1 hundred, 3 tens and 3 ones]

678: [67 tens and 8 ones], [60 tens and 78 ones], [6 hundreds, 7 tens and 8 ones]

877: [80 tens and 77 ones], [87 tens and 7 ones], [8 hundred, 7 tens and 7 ones]

543: [54 tens and 3 ones], [50 tens and 43 ones], [5 hundreds, 4 tens and 3 ones]

453: [45 tens and 3 ones], [40 tens and 53 ones], [4 hundreds, 5 tens and 3 ones]

341: [30 tens and 41 ones], [34 tens and one], [3 hundreds,4 tens and one]

555: [50 tens and 55 ones], [55 tens and 5 ones], [5 hundreds, 5 tens and 5 ones]

485: [48 tens and 5 ones], [40 tens and 85 ones], [4 hundreds, 8 tens and 5 ones]

789: [78 tens and 9 ones], [70 tens and 89 ones], [7hundreds, 8 tens and 9 ones]

864: [86 tens and 4 ones], [80 tens and 64 ones], [8 hundreds, 6 tens and 4 ones]

652: [65 tens and 2 ones], [60 tens and 52 ones], [6hundreds, 5 tens and 2 ones]

Here given an example to write a particular number in different representations.

13 tens and 12 ones = 13*10 + 12*1 = 130 + 12 = 142.

14 tens and 2 ones = 14*10 + 2*1 = 140 + 2 = 142.

1 hundred, 4 tens and 2 ones = 1*100 + 4*10 + 2*1 = 100 + 40 + 2 = 142.

So three representations are of number 142.

Rest blanks should be filled in same manner taking different numbers for each rows and three columns of each row should be filled with three different representation of that assumed numbers.

Representations for some numbers: