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
harkovskaia [24]
3 years ago
7

In a large population, 3% of the people are heroin users. A new drug test correctly identifies users 93% of the time and correct

ly identifies nonusers 90% of the time.Answer the following, showingall work for fullcredit.
a) Draw the probability tree for this scenario. Label the outcomes and indicate
b) What is the probability that a person who does not use heroin in this
c) What is the probability that a randomly chosen person from this population
d) What is the probability that a randomly chosen person from this population
e) If a person tests positive for heroin, what is the probability that he/she is a all the probabilities on the tree. population tests positive? is a heroin user and tests positive? tests positive? heroin user?
Mathematics
1 answer:
kari74 [83]3 years ago
6 0

Answer:

(a) The probability tree is shown below.

(b) The probability that a person who does not use heroin in this population tests positive is 0.10.

(c) The probability that a randomly chosen person from this population is a heroin user and tests positive is 0.0279.

(d) The probability that a randomly chosen person from this population tests positive is 0.1249.

(e) The probability that a person is heroin user given that he/she was tested positive is 0.2234.

Step-by-step explanation:

Denote the events as follows:

<em>X</em> = a person is a heroin user

<em>Y</em> = the test is correct.

Given:

P (X) = 0.03

P (Y|X) = 0.93

P (Y|X') = 0.99

(a)

The probability tree is shown below.

(b)

Compute the probability that a person who does not use heroin in this population tests positive as follows:

The event is denoted as (Y' | X').

Consider the tree diagram.

The value of P (Y' | X') is 0.10.

Thus, the probability that a person who does not use heroin in this population tests positive is 0.10.

(c)

Compute the probability that a randomly chosen person from this population is a heroin user and tests positive as follows:

P(X\cap Y)=P(Y|X)P(X)=0.93\times0.03=0.0279

Thus, the probability that a randomly chosen person from this population is a heroin user and tests positive is 0.0279.

(d)

Compute the probability that a randomly chosen person from this population tests positive as follows:

P (Positive) = P (Y|X)P(X) + P (Y'|X')P(X')

                  =(0.93\times0.03)+(0.10\times0.97)\\=0.1249

Thus, the probability that a randomly chosen person from this population tests positive is 0.1249.

(e)

Compute the probability that a person is heroin user given that he/she was tested positive as follows:

P(X|positive)=\frac{P(Y|X)P(X)}{P(positive)} =\frac{0.93\times0.03}{0.1249}= 0.2234

Thus, the probability that a person is heroin user given that he/she was tested positive is 0.2234.

You might be interested in
Find the probability that in a pig family of 4 offspring there will be at least 1 male and 1 female. Assume that the probability
Naya [18.7K]
The probability of there being zero males is given by:
P(zero\ males)=4C0\times0.5^{0}\times0.5^{4}=\frac{1}{16}
Similarly the probability of there being zero females is also 1/16.
The probability there will be at least 1 male and 1 female is therefore:
1-(\frac{1}{16}+\frac{1}{16})=\frac{7}{8}
The answer is: 7/8. 

5 0
3 years ago
Which graph is generated by this table of values?<br> PLS HURRY
viva [34]
Use two points to find the slope
8 0
2 years ago
Read 2 more answers
A movie rental company charges a yearly membership fee of $18.Each movie rental is $1.50.Which equation could be used to find th
Pavlova-9 [17]

Answer:

18+1.50m

Step-by-step explanation:

7 0
3 years ago
X squared minus 6x equals 0
Masja [62]

x²-6x=0

x(x-6)=0

Two solutions are possible:

x=0

x=6

8 0
3 years ago
30 POINTS PLEASE HELP!!! 4. The following equations represent the same quadratic function written in standard, vertex, and inter
sergij07 [2.7K]

Answer:

A

Step-by-step explanation:

So we have the quadratic equation and it's written in three equivalent forms:

f(x)=0.5x^2+x-1.5\\f(x)=0.5(x+1)^2-2\\f(x)=(0.5x+1.5)(x-1)

Let's determine the characteristics of the quadratic equation with the given equations.

From the first equation, since the leading coefficient (0.5) is positive, we can be certain that the graph opens upwards.

Also, the constant term is -1.5, so the y-intercept is (0,-1.5).

The second equation is the vertex form. Vertex form has the format:

f(x)=a(x-h)^2-k

Where (h,k) is the vertex. From the second equation we know that h is -1 (because (x+1) is the same as (x-(-1))) and k is -2. Therefore, the vertex is (-1,-2).

And since the graph points upwards, this means that (-1,-2) is the minimum point of the function. In other words, the range of the function is greater than or equal to -2. In interval notation, this is:

[-2,\infty)

This also means that the end behavior of the graph as a x approaches negative and positive infinity is positive infinity because the graph will always go straight up.

Also, the third form is the factored form. With that, we can solve for the zeros of the quadratic. The zeros are:

0.5x+1.5=0\text{ and } x-1=0\\0.5x=-1.5 \text{ and }x=1\\x=-3\text{ and }x=1

Therefore, the graph crosses the x-axis at x=-3 and x=1.

So, from the three equations, we gathered the following information:

1) The graph curves upwards.

2) The roots of zeros of the function is (-3,0) and (1,0).

3) The y-intercept is (0,-1.5).

4) The vertex is (-1,-2). This is also the minimum point.

5) Therefore, the range of the graph is all values greater than or equal to -2.

6) The end behavior of the graph on both directions go towards positive infinity.

Therefore, our correct answer is A.

B is not correct because the line of symmetry (or the x-coordinate of the vertex) here is -1 and not 1/2.

C is not correct because the graph goes towards <em>positive </em>infinity since it shoots straight up.

And D is not correct because the y-intercept is (0,-1.5).

3 0
3 years ago
Read 2 more answers
Other questions:
  • I need help and it is y intercept and x intercept
    5·1 answer
  • Find the exponential function that satisfies the given conditions: Initial value = 31, increasing at a rate of 10% per year
    11·1 answer
  • Providean explanation for each step 12d+2-3d=5
    13·1 answer
  • (9x+5h)2 2 is abve the parentheses answer is ______
    13·1 answer
  • Brynn ate 4/10 funnel cakes and 37/100 of the food was cotton candy. The rest of the food was popcorn. What fraction of the food
    7·1 answer
  • Anyone mind helping?
    11·1 answer
  • There Are 200 Employees In your company. Fifty of them do not have company health insurance . What Percentage Of the employees d
    14·2 answers
  • Na função definida por f(x)= 3x²-5x+6 seu gráfico é uma:
    7·1 answer
  • 8x+4(4x- 3) = 4(6x +4)-4​
    7·1 answer
  • Using the cross multiplication method what is the solution for 10/(x+2)=7/(x+2)
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!