Which probabilities are correct? select two options. p(a|c) = two-thirds p(c|b) = startfraction 8 over 27 endfraction p(a) = startfraction 31 over 59 endfraction p(c) = three-sevenths p(b|a) = startfraction 13 over 27 endfraction
Answers
Probability of an event is the measure of its chance of occurrence. The correct probabilities are:
P(A|C) = 2/3P(C) = 3/7How to interpret conditional probabilities?Suppose that the sample space is S. Out of which there are two events, A and B, subsets of S.
Then, we can interpret P(A|B) as the probability of that part of A which is in B, with the new sample space as B. (assuming probabililty of B isn't 0).
Symbolically, we write it as:
[tex]P(A|B) = \dfrac{P(A \cap B)}{P(B)}[/tex]
What is the size of the union of three sets?For three sets, A, B and C:
[tex]n(A \cup B \cup C) = n(A) + P(B) + P(C) - n(A\cap B) - n(A \cap C) - n(B \cap C) + n(A \cap B \cap C)[/tex]
The problem is incomplete. The corresponding venn diagram is attached below.
We can symbolize the venn diagram as:
[tex]n(A) = 12+8+6+5 =31\\n(B) = 11+8+5+3 = 27\\n(C) = 4+8+6+3 = 21\\n(A \cap B) = 5+8=13\\n(B\cap C) = 3+8=11\\n(A \cap C) = 6+8=14\\n(A \cap B \cap C) = 8[/tex]
S = sample space = collection of all unique elements.
S is union of A, B and C.
[tex]n(S) = n(A \cup B\cup C) = 31 + 27 + 21 -13-11-14+8 = 49[/tex]
Checking all the options for their correctness:
P(A|C) = 2/3We have:
[tex]P(A|C) = P(A\cap C)/P(C) = \dfrac{n(A\cap C)/n(S)}{n(C)/n(S)} = \dfrac{n(A \cap C)}{n(C)} = \dfrac{14}{21} =\dfrac{2}{3}[/tex]
Thus, its correct.
P(C|B) = 8/27[tex]P(C|B) = P(C\cap B)/P(B) = \dfrac{n(C\cap B)/n(S)}{n(B)/n(S)} = \dfrac{n(C \cap B)}{n(B)} = \dfrac{11}{27} \neq \dfrac{8}{27}[/tex]
Thus, this option is incorrect.
[tex]P(A) = \dfrac{n(A)}{n(S)} = \dfrac{31}{49} \neq \dfrac{31}{59}[/tex]Thus, this option is incorrect.
P(C) = 3/7[tex]P(C) = \dfrac{n(C)}{n(S)}= \dfrac{21}{49} =\dfrac{3}{7}[/tex]
Thus, its correct.
P(B|A) = 13/27[tex]P(B|A) = P(B\cap A)/P(A) = \dfrac{n(B\cap A)/n(S)}{n(A)/n(S)} = \dfrac{n(B\cap A)}{n(A)} = \dfrac{13}{31} \neq \dfrac{13}{27}[/tex]
Thus, this option is incorrect.
Thus, the correct probabilities are:
P(A|C) = 2/3P(C) = 3/7Learn more about probability here:
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Related Questions
The following table shows the heights, in inches, of the players on
the opening-night roster of the 2015-2016 New York Knicks.
84
80
87
75 77
79
80
74 76 80
80
82
82
The population standard deviation of these data is approximately
(1) 3. 5
(3) 79. 7
(2) 13
(4) 80
Answers
If the value of the mean is 79.6923 then the standard deviation is 3.5. Then the correct option is A.
What is a standard deviation?It is the measure of the dispersion of statistical data. Dispersion is the extent to which the value is in a variation.
The following table shows the heights, in inches, of the players on the opening-night roster of the 2015-2016 New York Knicks.
84, 80, 87, 75, 77, 79, 80, 74, 76, 80, 80, 82, 82
The mean will be
N = 13
[tex]\mu = \dfrac{84+ 80+ 87+ 75+ 77+ 79+ 80+ 74+ 76+ 80+ 80+ 82+ 82}{13}\\\\\mu = \dfrac{1036}{13}\\\\\mu = 79.6923[/tex]
Then the standard deviation will be
[tex]\sigma = \sqrt{\dfrac{\Sigma _{i=2}^N (x_i - \mu)^2}{N}}\\\\\sigma = \sqrt{\dfrac{(84-79.6923)^2+(80-79.6923)^2+ ..... + (82-79.6923)^2}{13}}\\\\\sigma = 3.4947128281848 \approx 3.5[/tex]
More about the standard deviation link is given below.
https://brainly.com/question/12402189
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Between 1966 and 1976 by what percentage did the average number of passengers per aircraft increase?
A 38
B 58
C 61
D 137
Answers
Answer:
C 61
Step-by-step explanation:
Find the area of the shaded region.
Answers
Answer:
Step-by-step explanation:
Remark
The method of finding the area of the ring is to find the area of the outer ring and subtract the area of the hole in the middle.
Outer ring
r = 10 + 4 = 14 inches
Area = pi * r^2
Outer ring area = pi * 14^2
Outer ring area = 196 pi
Inner hole
Area unshaded part = pi * r^2
r = 10
Area = pi * 10^2
Area = 100 pi
Area of the shaded part
area of the shaded part = outter circle area - inner circle area
outter circle area = 196 * pi
inner circle area = 100 pi
Area of the shaded part = 196 pi - 100 pi
Area of the shaded part = 96 pi
pi = 3.14
Area of the shaded part = 96 * 3.14
Answer area of the shaded part = 301.44
Answer area of the shaded part = 301.4 rounded to the nearest tenth
The second problem is done exactly the same way. Only the numbers have been changed. I will give you the answers to the main part of the problem and you can try and get what I got. If we disagree, be preparred to tell me what you got so I correct mine if it is wrong.
Outter Radius = 18 + 8 = 26
Area of outter circle = pi * 26^2
Area of outter circle = 676 pi
Inner Circle area hole = pi * 18^2
Inner Circle area hole = 324 pi
Area of the shaded part = outter circle - inner circle
Area of the shaded part = 676 pi - 324 pi
Area of the shaded part = 352 pi
pi = 3.14
Area of the shaded part = 352 * 3.14
Answer: area of shaded part rounded to 1 decimal place = 1105.3
A used car lot sold 12 minivans last month, along with 54 other vehicles. Considering this data, how many of the next 77 vehicles sold should you expect to be minivans?
47 points and brainiest to the answer!
Answers
Find percentage of minivans.
12/66 = 0.1818 or ~18%
~18% of 77
77* 0.1818 = 13.999 ~ 14 rounded
what do 12x4x3x5÷2×6 30 points and brainliest.
Answers
Answer:
2160
Step-by-step explanation:
12×4×3×5÷2×6
Multiply 12 and 4 to get 48.
2
48×3×5
×6
Multiply 48 and 3 to get 144.
2
144×5
×6
Multiply 144 and 5 to get 720.
2
720
×6
Divide 720 by 2 to get 360.
360×6
Multiply 360 and 6 to get 2160.
2160
Answer:
follow PEMDAS
parentheses not included in this problemexponents not included in this problemmultiplicationdivisonaddition not included in this problemsubtraction not included in this problemthat leaves multiplication as our first priority, division as our second.
[tex]12 * 4 = 48\\48 * 3 = 144\\144 * 5 = 720\\solve~2 * 6\\2 * 6 = 12\\now~resume\\12 / 720 = 60[/tex]
I NEED HELP PLSS I HAVE NOO TIME LEFT
Answers
Step-by-step explanation:
x/15 = y/6
x = 15y/6
x/y = 15/6 = 5/2
what is the quotient and remainder for 56,677 divided by 8
Answers
Answer:
quotient: 7084
remainder: 5
16. The ordered pairs below represent a linear
function.
(2,64), (14,77), (x, y)
Which values could be the values of x and y?
Answers
How do we most easily graph an equation in the form Ax+By=C? Explain, and use at least one example.
Answers
Answer:
Rewrite the equation into the form of "y=mx+b", plot the y-intercept (b), plot the x-intercept(s), then create the line.
Step-by-step explanation:
Example: 2x + y = 1
Rewrite: y = -2x + 1Plot y-intercept: (0, 1)Plot x-intercept: (1/2, 0)Draw lineI hope this helps!
Solve this and get points please . :)
6 + 3 x 2 - 5 +( 7 - 1 )
And try Ur best , remember to work at a good pace and take Ur time.
Answers
Answer:
13
Step-by-step explanation:
6+3 x 2-5+(7-1)
6+3 x 2-5+(6)
6+6-5+6
12-5+6
7+6
13
[tex]6 + 3 \times 2 - 5 + (7 - 1)[/tex]
solution:you can follow BODMAS rule where,
B= brackets
O= Order
D= Division
M= Multiplication
A= Addition
S= Subtraction
let's solve:[tex]6 + 3 \times 2 - 5 + (7 - 1)[/tex]
[tex] = 6 + 3 \times 2 - 5 + 6[/tex]
[tex] = 6 + 6 - 5 + 6[/tex]
[tex] = 12 - 5 + 6[/tex]
[tex] = 7 + 6[/tex]
[tex] = 13[/tex]
A car tyre has a diameter of 60 cm.
How far will the wheel travel in one revolution?
Answers
Answer:
Step-by-step explanation:
If 60cm is the outer diameter of the rim, then the rim without a tire would travel 188.50 (not 188.4) cm per revolution. There will of course be a tire, and the extra diameter of wheel+tire will increase the distance traveled by the bike. If e.g. the tire is 3cm from bead to outermost tread (and is properly inflated), then the extra circumference would be 2 x 3cm x pi = 18.850cm of distance traveled, for a total of just over 207.3 cm per revolution.
This triangular prism is 22 inches tall and has a base with an area of 60 square inches. What is the volume of the prism?
ANSWER CHOICES:
1320 cubic inches
82 cubic inches
660 cubic inches
729,000 cubic inches
ANSWER QUICKLY
Answers
Answer:
A 1320
Step-by-step explanation:
22 x 60
1320
Jason has two bags with 6 tiles each. The tiles in each bag are shown below:
Six squares are numbered sequentially from 1 to 6.
Without looking, Jason draws a tile from the first bag and then a tile from the second bag. What is the probability of Jason drawing an even tile from the first bag and an even tile from the second bag?
6 over 12
9 over 12
6 over 36
9 over 36
Answers
Answer:
9/36
Step-by-step explanation:
Given :1,2,3,4,5,6
first draw even probability 3/6=1/2
second draw even probability 3/6=1/2
1/2x1/2 or 3/6 x3/6= 1/4 or 9/36
Two similar solids have a surface areas of 48ft^2 and 147ft^2 respectively. If the volume of the smaller solids is 320ft^3, what is the volume of the larger solid?
Answers
Two similar solids have a surface area of 48ft^2 and 147ft^2 respectively. If the volume of the smaller solids is 320ft^3 and the volume of the larger solid is 1715 cubics in.
What is a triangle?A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.
Two similar solids have a surface area of 48ft^2 and 147ft^2 respectively.
If the volume of the smaller solids is 320ft^3.
Since the solids are similar, the ratio of the surface areas is equal to the square of the scale factor, k.
Thus, k2 = 147 / 48 , or k = 49/16 = 7/4
The ratio of the volumes of the solids is equal to k3, which gives:
V / 320 = (7/4)^3
where V is the volume of the larger solid.
V = 320 x (7/4)^3
= 1715 cubics in
Learn more about volume;
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Please help me with this math problem!! Will give brainliest!! NO LINKS PLEASE!! Thanks!! :)
Answers
Answer:
Step-by-step explanation:
arc EF=90-20=70°
arc FDA=20°
∠ABC==180-20=160°
Please solve this equation
Answers
Answer
(1 - sin2x)/(sin - 1)
Step-by-step explanation:
tan225° = 1
sin270° = -1
Substitue these values and you get:
(1 - sin2x)/(sin - 1)
Hope this helps!
. A set of trading cards sells for $8.95
before tax. After sales tax, it costs
$9.60. What is the sales tax rate?
Answers
mean of of 0, 3, and 6
Answers
Answer:
3
Step-by-step explanation:
Mean= add up all the numbers, then divide by how many numbers there are. 0+3+6=9
9/3=3
Steve is turning half of his backyard into a chicken pen. His backyard is a 24 meter by 45 meter rectangle
Answers
Subtract. Write your answer in lowest terms.
Wirte the working steps
Answers
Answer:
7/15
Step-by-step explanation:
First, find the common denominatorHere it’s 5 * 3, which is 15You times 5 by 3 to get 15, so times the 4 by 3 as well to make sure that the fraction is equivalent4/5 now becomes 12/15Now for 1/3You times 3 by 5, so times 1 by 5This gives 5/15Just subtract the numerators now since they now have the same denominator12/15 - 5/15 = (12-5)/15 = 7/15-10(x – 7) – 3x simplified
Answers
5.7 times -4.2. step by step
Answers
Answer:
5.7×-1.2=-7.14
Step-by-step explanation:
+5.7(×)-1.3
+(×)- = -(it gives a negative answer)
so you multiply 5.7 and 1.3= 7.14
you just add a negative sigh to the ans
answer=-7.14
please consider a brainlest question
A school district is considering a change that would involve switching the daily start times for its elementary and
high schools. Administration wants to take a sample of parents from each type of school and perform a two-
sample test to see if the proportion who support the change is significantly different between the two groups.
Which of the following are conditions for this type of test?
Answers
Using the Central Limit Theorem, it is found that each random sample must have at least 10 parents supporting the change and 10 opposing.
What does the Central Limit Theorem state?It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].
For the test hpyothesis, two conditions are needed:
Random samples.The sampling distribution must be approximately normal.Hence each random sample must have at least 10 parents supporting the change and 10 opposing.
More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213
Could I get some help on this?
Answers
Answer:
200.5ft²
Step-by-step explanation:
According to my calculation this is the answer ..
Why is Pluto not a planet? Give at least 2 reasons why it was moved to a dwarf planet status.
Answers
Answer:
1.) It's too small to be considered a planet.
2.)it did not meet the three criteria the IAU uses to define a full-sized planet.
Find the 14th term in the following sequence: -1, -3, -5, -7, ..
Answers
Answer:
[tex]t_{14}[/tex]= -27
Step-by-step explanation:
a = -1
and d = -3 - (-1)
= -2
Basically, [tex]t_{14}[/tex] = a + 13d
= -1 + 13 x (-2)
= -1 - 26
= -27
Nile’s places £4000 in a bank account that pays 2.5% simple interest per year how much interest will he earn in 4 years
Answers
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \pounds 4000\\ r=rate\to 2.5\%\to \frac{2.5}{100}\dotfill &0.025\\ t=years\dotfill &4 \end{cases} \\\\\\ I = (4000)(0.025)(4)\implies I=400[/tex]
10. A triangular pyramid has a volume of 60 cubic centimeters. The
triangular base has a 12-centimeter base and a 5-centimeter height. Find the
height of the pyramid.
Explain
Answers
Answer:
3 cm
Step-by-step explanation:
The formula for the volume of a pyramid is :
V = [tex]\frac{Ah}{3}[/tex]Given
Volume = 60 cm³Base Area = 12 cm x 5 cm = 60 cm²Solving
60 = 60 x h x 1/360 = 20hh = 60/20 = 3 cm3/5•3/5•3/5=?
3/5•5/5•4/5=?
Please?
Answers
3 • 3 • 3 / 5 • 5 • 5
27/125
3 • 5 • 4 / 5 • 5 • 5
60/125
simply if needed
12/25
it’s very simple you’re welcome fellow learner :)
Answer:
1) 27/125
2) 12/25
Step-by-step explanation:
3*3*3 = 27
3*5*4= 60, but simplified is 12/25
is 2/100the fractional form of 0.02??
Answers
Answer:
Yes it is
Step-by-step explanation:
2/100 = 0.02
You have to move two spaces to the left of 2, as 100 contains two zeroes (u must start counting from 2 and put zeroes along, until u finish counting)
after u finish counting put a 0. in the left of of all the zeroes and the 2