Answer:
0.0748 = 7.48% probability that he is guilty
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Tests indicates guilty
Event B: Person is guilty
Probability that the test indicates that the person is guilty:
4/5 = 0.8 of 1/100 = 0.01(person is guilty)
1 - 0.9 = 0.1 of 1 - 0.99(person is not guilty). So
[tex]P(A) = 0.8*0.01 + 0.1*0.99 = 0.107[/tex]
Test indicates guilty and the person is guilty;
0.01 of 0.8. So
[tex]P(A \cap B) = 0.01*0.8 = 0.008[/tex]
What is the probability that he is guilty?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.008}{0.107} = 0.0748[/tex]
0.0748 = 7.48% probability that he is guilty
The required value is [tex]\simeq0.925 \ or \ 92.5[/tex]%.
Probability:Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are to happen, using it.
Let [tex]T_G[/tex] and [tex]T_I[/tex] denote the test result being guilty or innocent respectively.
And, [tex]G[/tex] and [tex]I[/tex] denote that the person is guilty or innocent respectively.
Given that: [tex]P\left ( T_G\mid I \right )=\frac{4}{5}[/tex]
[tex]P\left ( T_I\mid I \right )=\frac{9}{10}\Rightarrow P\left ( T_G\mid I \right )=1-\frac{9}{10}=\frac{1}{10}[/tex]
[tex]P(G)=\frac{1}{100} \\ \therefore P(I)=1-P(G) \\ =1-\frac{1}{100} \\ =\frac{99}{100}[/tex]
Now, the required probability is,
[tex]P(I\mid T_G)=\frac{P\left ( T_G\mid I \right )\times P(I)}{P(T_G\mid I)\times P(I)+P\left ( T_G\mid G \right )\times P(G)}[/tex]
[tex]=\frac{\frac{1}{10}\times\frac{99}{100}}{\left ( \frac{1}{10}\times \frac{99}{100}\right )+\left ( \frac{4}{5}\times\frac{1}{100} \right )} \\ =\frac{0.099}{0.099+0.008} \\ =\frac{0.099}{0.107} \\ =0.92523 \\ \simeq 0.925 \\ or \ 92.5%[/tex]
Learn more about the topic of Probability: brainly.com/question/26959834
please help me someone i really need this to get my grade up :(
Answer: D
2 1/2 divided by 1/4 = 10
hope this gets ur grade up keep trying ur best!! :D
Please help please please
Answer:
1078m²
Step-by-step explanation:
Formulas:
Total Surface Area = 2B + Ph
Area = 1/2bh
Solve:
19 × 17 = 323
19 + 19 + 17 + 17 = 72
h = 6m
B = 323m
P = 72m
Total Surface Area = 2(323m) + (72m × 6m) = 1078m²
1.ILL GIVE BRAINIEST FOR ANSWER
Chan invested $12,500 in a savings account that pays 2.5% simple interest. How much interest does
he earn each year?
F $350.50
G $312.50
H $322.50
J $325.50
Answer:
Step-by-step explanation:
What is the solution of the equation z +8 = 21?
Answer: 13
Explanation:
21-8=13
z = 13 is the solution of the equation z +8 = 21.
What is simplification?When a mathematical expression is converted into an equivalent, typically shorter statement, it becomes simpler. Procedure simplification is one method to encourage uniformity in work effort, expense, and duration. It reduces diversity and variation that is detrimental, pointless, or unnecessary.
Given, an expression z + 8 = 21
Simplifying it,
z = 21 - 8
z = 13
Therefore, The answer to the equation z + 8 = 21 is z = 13.
Learn more about simplification here:
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Find the volume of the sphere. Round to the nearest tenth.
The volume is about _____ cubic meters.
find the volume if the cylinder. round to the nearest tenth if nessesary.
A. 627.5m^3.
B. 843.4m^3.
C. 986.4^3.
D. 1017.9n^3
A retail shop is replacing their flooring with laminate wood. The floor plan is shown below. Determine the total square feet of laminate wood needed to complete the the job.
Answer:
1075 ft
Step-by-step explanation:
25*35 = 875
8*25 = 200
875+200 = 1075
Does the equation below represent a relation, a function, both a relation and a function or neither
y = x2 – 9x
An air conditioning system can circulate 430 cubic feet of air per minute. How many cubic yards of air can it circulate per minute?
Divide the number of cubic feet that it can circulate by the number cubit feet per cubic yard. That gives the number of cubic yards that it can circulate. It can circulate about 10.37 cubic yards per minute.
The air conditioning system can be circulate in 15.92 cubic yards of air per minute.
Here,
An air conditioning system can circulate 430 cubic feet of air per minute.
We have to find the cubic yards of air which can be circulate in per minute.
What is the value of cubic yard in cubic feet?
1 cubic yard = [tex](3 ft)^3[/tex] = 27 cubic feet.
Now,
1 cubic yard = [tex](3 ft)^3[/tex] = 27 cubic feet.
Hence, Cubic yards of air circulate in per minute = 430/27 = 15.92
So, The air conditioning system can be circulate in 15.92 cubic yards of air per minute.
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What's the height if a triangle with area of 20 units2
Answer:
10
Step-by-step explanation:
20/2=10
Mark hsa a square photo with an area of 9cm squared.
He enlarged the photo to have an area of 36 cm squared
To do this the length of each side was multiplied by a factor of
two three four five or six?
Answer:
4
Step-by-step explanation:
36/9=4
A fish aquarium is 3 ft long, 2 ft wide, and 2 ft high. What is the volume of the aquarium?
ANSWER ASAP I DONT HAVE MUCH TIME
what % of 4 is 7
i need this to be answered as quickly as possible please
Answer:
the answer
= 17.5
Step-by-step explanation:
https://www.percentagecal.com/answer/.7-is-what-percent-of-4#:~:text=Percentage%20Calculator%3A%20.,%3D%2017.5
2(5+xi)-21+5i=3yi^2-3yi
Answer:
x = -8, y = 11/3
Step-by-step explanation:
65% of the total number of students are girls and there are 224 boys. find the percent of boys ? find the number of girls?
40 POINTS !! 40 POINTS !!
PLEASE HELP , DONT SKIP !
NO LINKS OR FILES.
Answer: The answer is 4 pieces of chalk
Answer:
7 chalks
Step-by-step explanation:
7 crosses are above numbers that are higher than 5
Solve the following radical equation , Show work also please !
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{-12=6\sqrt{x+4}}[/tex]
[tex]\mathsf{6 \sqrt{x + 4}=-12}[/tex]
[tex]\textsf{DIVIDE your BOTH SIDES by 6}[/tex]
[tex]\mathsf{\dfrac{6\sqrt{x + 4}}{6}= \dfrac{-12}{6}}[/tex]
[tex]\textsf{Introduce the new temporary equation}[/tex]
[tex]\mathsf{\sqrt{x + 4}=-2}[/tex]
[tex]\textsf{SOLVE for your SQUARE ROOT }[/tex]
[tex]\mathsf{\sqrt{{x + 4}}=-2}[/tex]
[tex]\mathsf{Like: x + 4 = (-2)^2}[/tex]
[tex]\textsf{SQUARE EACH of your SIDES}[/tex]
[tex]\mathsf{x + 4 = 4}[/tex]
[tex]\textsf{SUBTRACT your BOTH SIDES by 4 }[/tex]
[tex]\mathsf{x + 4 -4= 4-4}[/tex]
[tex]\mathsf{Cancel\ out\ 7-7 \ because\ it\ gives\ you\ 0}[/tex]
[tex]\textsf{Solving for your last temporary question}[/tex]
[tex]\mathsf{x = 4-4}[/tex]
[tex]\mathsf{4-4 = \bf 0}[/tex]
[tex]\mathsf{\bf x = 0}[/tex]
[tex]\textsf{Plug your x-value (x = 0) to make sure it works for your original equation}[/tex]
[tex]\textsf{You will see that it doesn’t work for the original problem so this means that the}\\\textsf{original equation \bf does NOT have any solutions.}[/tex]
[tex]\boxed{\boxed{\large\text{Answer: \huge\bf No solutions}}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
How does the stimulus check impact society please help me please i really need help please
Answer:
It helps families who or who do not have the resources and helps them with money issues
Step-by-step explanation:
hope it helps
What is 10×25 to the sixth power
Answer:
2.4414063e+14 (wow such a large number)
Step-by-step explanation:
10x25= 250
250 to the 6th power = 2.4414063e+14
Simplify 4^3 • 4^5
a 4^8
b 16•15
c 4^15
d 16^8
Answer:
4^8
Step-by-step explanation:
keep base (which is 4) and add exponents when multiplying
helppppppppppppppppp
Answer:
x[tex]\leq[/tex]1
Step-by-step explanation:
I. NEED. HELP. NOW. PLEASE.
THIS IS DUE IN 3 HOURS
Answer:
1. $670
2.$920
3.$1500
4.$2100
Step-by-step explanation:
Hope it was fast enough & helpful .
Good luck ^^
Find the value of the trig function indicated
Answer:
A. (2√13)/13
Step-by-step explanation:
Recall, SOHCAHTOA.
Thus,
Cos θ = Adjacent/Hypotenuse
Adjacent = 16
Hypotenuse = 8√13
Therefore,
Cos θ = 16/(8√13)
Rationalize
Cos θ = (16*√13)/(8√13*√13)
Cos θ = (16√13)/(8*13) = (2√13)/13
which equation has a slope of -1/4?
A) y=4
B) y=-4x
C) y=-1/4x+1
D) y=4x+9
E) x=-1/4
F) y=-1/4
Answer:
C
Step-by-step explanation:
y = mx + b
Choice C is y = (-1/4)x + 1
m or slope = -1/4
The "middle" term of the trinomial form of (3x + 5)(4x – 3)
is:
29x
- 3x
O 11x
0 2x
I want the answer the steps
Answer:
The "middle" term is 11x.
Step-by-step explanation:
(3x + 5)(4x - 3)
Solve this by using FOIL: first – outer – inner – last
F: 3x • 4x = 12x²
O: 3x • -3 = -9x
I: 5 • 4x = 20x
L: 5 • -3 = -15
Combine the terms.
12x² - 9x + 20x - 15
Combine like terms.
12x² + 11x - 15
The "middle" term is 11x.
Hope this helps!
ANSWER ASAP! SCAM LINKS REPORTED.
Answer:
b is correct
Step-by-step explanation:
i did this pls mark as branlyest
Answer:
I believe the answer is D
Step-by-step explanation:
Solve 4r2 – 5 = 59
{± 3}
{± 4}
{± 5}
{±6}
9514 1404 393
Answer:
(b) ±4
Step-by-step explanation:
4r^2 -5 = 59 . . . . given
4r^2 = 64 . . . . . . . add 5
r^2 = 16 . . . . . . . . . divide by 4
r = ±4 . . . . . . . . . . . take the square root
How much money is needed to be invested now to obtain $12,100 8 years from now if this amount is invested at 7.25% compounded continuously?
Answer:
$6,911.92
Step-by-step explanation:
Given the following
Amount A = $12,100
Time t = 8yrs
Rate r = 7.25%
Required
Principal P
Using the compound interest formula;
A = P(1+r)^n
12,100 = P(1+0.0725)^8
12,100 = P(1.0725)^8
12100 = 1.7506P
P = 12,100/1.7506
P = 6,911.92
Hence the amount invested would have been $6,911.92
Which choice is equivalent to the expression below?
✓-27
A. -3✓3
B. 3✓3
C. 3i✓3
D. -✓27
E.-3✓3i
Answer:
C. 3i✓3
Step-by-step explanation:
Which choice is equivalent to the expression below?
✓-27
Square root of a negative value, so it will have a complex part.
We have that:
[tex]\sqt{-a^2} = ai[/tex]
In this question:
The square root of -27 can be factored as:
[tex]\sqrt{-27} = \sqrt{3(-9)} = \sqrt{3}\sqrt{-9} = 3i\sqrt{3}[/tex]
So the correct answer is given by option C.
If f(x)=x squared-2x and g(x) = 6x+4 for which is a value of x does (f+g)(x) =0
Answer:
For [tex]x = -2[/tex]
Step-by-step explanation:
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]
[tex]\Delta = b^{2} - 4ac[/tex]
In this question:
[tex]f(x) = x^2 - 2x[/tex]
[tex]g(x) = 6x + 4[/tex]
[tex]f(x) + g(x) = (f+g)(x) = x^2 - 2x + 6x + 4 = x^2 + 4x + 4[/tex]
Which is a value of x does (f+g)(x) =0
[tex]x^2 + 4x + 4[/tex]
Quadratic equation with [tex]a = 1, b = 4, c = 4[/tex]
So
[tex]\Delta = 4^{2} - 4*1*4 = 0[/tex]
[tex]x_{1} = \frac{-4 + \sqrt{0}}{2} = -2[/tex]
[tex]x_{2} = \frac{-4 - \sqrt{0}}{2} = -2[/tex]
For [tex]x = -2[/tex]