Answers
8. For brevity, let U = unemployed, E = employed, M = male, F = female. We're given that
P(M) = P(F) = 50/100 = 1/2
P(U) = 60/100 = 3/5
P(M | U) = 2/3
P(E) = 40/100 = 2/5
P(F | E) = 3/4
8a. This follows immediately from the given information. Specifically,
P(E) = 1 - P(U) = 1 - 3/5 = 2/5
8b. By definition of conditional probability,
P(A | B) = P(A and B) / P(B) ⇒ P(A and B) = P(A | B) P(B)
It follows that
P(M and U) = P(M | U) P(U) = 2/3 • 3/5 = 2/5
8c. Using Bayes' rule/the definition of conditional probability,
P(U | F) = P(U and F) / P(F) = P(F | U) P(U) / P(F)
Since F and M are mutually exclusive,
P(F | U) = 1 - P(M | U)
and so
P(U | F) = (1 - 2/3) • 3/5 / [(1 - 2/3) • 3/5 + 3/4 • 2/5] = 2/5
8d. Here we assume gender and employment status are independent, so for instance
P(F and E) = P(F) P(E)
We then have by the inclusion/exclusion principle that
P(F or U) = P(F) + P(U) - P(F and U) = P(F) + P(U) - P(F) P(U)
We also have by the law of total probability
P(F) = P(F and U) + P(F and E)
so
P(F or U) = P(F and U) + P(F and E) + P(U) - P(F) P(U)
By the assumed independence,
P(F or U) = P(F) P(U) + P(F) P(E) + P(U) - P(F) P(U)
P(F or U) = P(F) P(E) + P(U)
P(F or U) = 1/2 • 2/5 + 3/5 = 4/5
9.
a. This is mostly a matter of counting the ways a given type of stamp can fall out.
[tex]P(A) = \dfrac{\dbinom{20}3}{\dbinom{24}3} = \dfrac{285}{506}[/tex]
since there are 20 non-green stamps.
[tex]P(B) = \dfrac{\dbinom21 \dbinom{22}2}{\dbinom{24}3} = \dfrac{21}{92}[/tex]
since there are 2 red and unused stamps, 1 of which we want; the other 2 stamps come from the remaining 22 non-red-and-unused stamps.
[tex]P(A \cap B) = \dfrac{\dbinom21 \dbinom{18}2}{\dbinom{24}3} = \dfrac{153}{1012}[/tex]
since exactly 1 of the stamps must be red and unused, and the other 2 stamps that fall out can be neither green nor red and unused.
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B) = \dfrac{162}{253}[/tex]
which follows from the inclusion/exclusion principle.
b. There is a total of 10 used stamps, so the probability of at least 1 going missing is
[tex]P(C) = \dfrac{\dbinom{10}1\dbinom{14}2 + \dbinom{10}2\dbinom{14}1 + \dbinom{10}3}{\dbinom{24}3} = \dfrac{415}{506}[/tex]
By definition of conditional probability,
[tex]P(C \mid A) = \dfrac{P(C \cap A)}{P(A)}[/tex]
However, there are no used green stamps; any used stamp that goes missing must be red, blue or yellow. So the event A ∩ C is really just the event C, and
[tex]P(C \mid A) = P(C) = \dfrac{415}{506}[/tex]
c. A and C are independent if and only if
[tex]P(A \cap C) = P(A) P(C)[/tex]
We know
[tex]P(C \cap A) = P(C)[/tex]
so if A and C are independent, then
[tex]P(C) = P(A) P(C)[/tex]
but this would imply P(A) = 1, which is clearly not the case as we found in 9.a. So A and C are not independent.
Related Questions
Scott has 2 six-sided dice. What is the probability that the sum of the roll is one?
Answers
Answer: 0, it’s not possible to roll 2 dice with the sum ending up being one.
Which of the following functions is equal to f(x)=csc(x-9pi)+2 ? Select 3 answers
Answers
B. f(x) = csc(x - pie ) + 2 = - csc(x) + 2
C. f(x) = - csc(x - 2pie) + 2 = - csc(x) + 2
F. f(x) = - sec(x - 9pie/2 ) + 2 = - sec( x - 4pie - pie/2 ) + 2
= - sec(x - pie/2) + 2 = - csc(x) + 2
I NEED HELP ASAP!!!!!
Answers
2= not polynomial
3= polynomial
4= polynomial
5= not polynomial
6= polynomial
Express the difference between 0.35 and 2/5 as a decimal
Answers
0.05
Explanation:
2/5 is as a decimal, 0.4
The difference between them is 0.05
If you are traveling in your car at an average rate of r miles per hour for T hours, then the distance d in miles that you travel is described by the formula d=rt that is distance equals rate times time. A distance of 60 miles at an average rate of 40 miles per hour is covered in ___ hours?
Answers
Answer:
1.5 hr
Step-by-step explanation:
d = rt
re-arrange to
d/r = t
60 miles / 40 miles/hr = 1.5 hr
Help picture below problem 13
Answers
Answer:
B. Obtuse
Step-by-step explanation:
An obtuse angle is defined as one that extends beyond 90 degrees. An acute angle is defined as one that is less than 90 degrees. A right angle is one that is 90 degrees.
need help with geometry (number 20)
Answers
Answer: A
Step-by-step explanation:
Since diagonals of a rectangle are congruent and bisect each other, we know that the two opposite triangles formed by the diagonals are congruent by SAS.
Therefore, the measure of angle 1 is equal to 25 degrees.
A club swimming pool is 22 ft wide and 44 ft long. The club
members want an exposed aggregate border in a strip of
uniform width around the pool. They have enough material for
432 ft squared. How wide can the strip be?
Answers
Answer:
968 is what they need and no they do not enough material
Step-by-step explanation:
What I always do on these questions is length times width and they need 536 more material
can someone please help me out with this logarithm equation
Answers
[tex] \green{ - - - - - - - - - - - - - - - - - - }[/tex]
•— QUESTIONLogarithmic equation : log2 + log x = 1•— ANSWERThe answer is x = 5•— SOLUTIONlog¹⁰2+ log¹⁰ x = 1x >0log¹⁰2 + log¹⁰ x = 12x = 10[tex] \times \frac{10}{2} [/tex]x = 5•— Therefore, the answer is x = 5
[tex] \green{ - - - - - - - - - - - - - - - - - - }[/tex]
A triangular swimming area is marked off by a rope.
a. If a woman swims around the perimeter of the swimming area, how far will she swim?
b. What is the area of the roped off section?
Answers
Δ perimeter of swimming area:
total length measure of all sides200√3 + 200√6 + 400 + 200( 200√3 + 200√6 + 600 ) m1436.3 mΔ area of roped off section:
1/2 base * height1/2 * (200+200√3)(200√3)20000√3 + 60000 m²94641 m²Please help!!!
John's water bill this month was $19.67. Looking at the water bill, it says he used exactly 10,000 gallons of water. How much does he pay per gallon of water used?
Answers
Answer:
$0.001967/gallon
Step-by-step explanation:
John uses alot of water.... and it sure is cheap.
19.67/10000 =
Round your answer to the nearest hundredth.
Answers
Answer:
67.98°
Step-by-step explanation:
Hope this helps! Please let me know if you need more help or think my answer is incorrect. Brainliest would be MUCH appreciated. Also remember to rate answers to help other students, While leaving thanks to answers that help you. Have a great day!
A mother decides to teach her son about a letter each day of the week. She will choose a letter from the name of the day. For example, on Saturday she
might teach about the letter S or the letter U, but not the letter M.
Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
What letters are CANT BE TAUGHT using this method? (There are 11.)
ОА
OB
Ос
OD
ОЕ
OF
OH
01
Answers
Answer:
01 she can teach alphabet using seven days name but not numbers.
PLEASE ONLY ANSWER B. (GIVING BRAINLIEST THANKS)
Answers
Answer:
[tex][7\times(-2)]^5 = 7^5 \times (-2)^5[/tex]
Step-by-step explanation:
how can I solve 1 4/5 x 1/2?
Answers
Answer:
[tex]\frac{9}{10}[/tex]
Step-by-step explanation:
first we write 1 4/5 as an improper fraction:
[tex]1 \frac{4}{5}=\frac{5}{5}+\frac{4}{5}=\frac{5+4}{5}=\frac{9}{5}[/tex]
Now we multiply :
[tex]\begin{aligned}1 \frac{4}{5} \times \frac{1}{2} &=\frac{9}{5} \times \frac{1}{2} \\&=\frac{9 \times 1}{5 \times 2} \\&=\frac{9}{10}\end{aligned}[/tex]
3. The weight of cell phones is normally distributed. The mean weight of a sample of 300 cell phones is 112 grams, with a standard deviation of 2 grams. With a 95% confidence level, determine
the maximum error of estimate
18.99%
22.63%
1.31%
29.73%
Answers
The maximum error of estimate with a sample of 300 cell phones is 29.73%
Determining maximum error estimateThe formula for calculating the maximum error of the estimate is expressed as:
ME = √0.25/n
n is the total sample
Given the following parameters
n = 300
Substitute into the formula to have:
ME = √0.25/n
ME = √0.25/300
ME = 0.2973
ME = 29.73%
Hence the maximum error of estimate with a sample of 300 cell phones is 29.73%
Learn more on maximum error here: https://brainly.com/question/13370015
The weight of cell phones is normally distributed. The mean weight of a sample of 300 cell phones is 112 grams, with a standard deviation of 2 grams. With a 95% confidence level, determine
the maximum error of estimate
Answer:
29.73%
What’s the circumference of circles
Answers
Answer:
62.83185
Step-by-step explanation:
C=2πr=2·π·10≈62.83185
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Circumference of circle is :
[tex]\qquad \tt \dashrightarrow \:\pi d[/tex]
where,
d = diameter of circle[tex]\qquad \sf \dashrightarrow \:c = 20 \pi \: \: cm[/tex]
Now, let's plug approximate value of pi
[tex]\qquad \sf \dashrightarrow \:c = 20 \times 3.14\: \: [/tex]
[tex]\qquad \sf \dashrightarrow \:c = 62.8 \: \: cm[/tex]
Please help as fast as possible
Answers
[tex]\rm Answer:[/tex]
20.125%
To find the relative frequency, divide the frequency(f) by the total number of data values (n).[tex]\rm \# KiroToshiroComeback[/tex]
A, B, C, D are points on a line.
AB = 1
BC = 2
CD = 4
Find the length of segment AD. Consider all possibilities.
So far, I've only gotten 7, 5, and 1. But I know there is one left. Can you guys help?
Answers
The points A, B, C and D are collinear points
The length of the segment AD is 7 units
How to determine the length AD?The given parameters are:
AB = 1
BC = 2
CD = 4
Because the points are on the same line, then the following is the possible equation
AD = AB + BC + CD
Substitute known values
AD = 1 + 2 + 4
Evaluate the sum
AD = 7
Hence, the length of the segment AD is 7 units
Read more about line segments at:
https://brainly.com/question/14366932
Please help solve questions
Answers
Take some points
2x+3y<63y<-2x+6y<-2/3x+2As here < sign present line will be dashed and shading should be done below the line
So
(1,1)(1,0)(2,0)(-1,2)Graph attached
Answer:
Given inequality
[tex]\sf 2x + 3y < 6[/tex]
Rearrange to make y the subject
[tex]\sf \implies 2x + 3y < 6[/tex]
Subtract 2x from both sides:
[tex]\sf \implies 3y < -2x + 6[/tex]
Divide both sides by 3:
[tex]\sf \implies y < -\dfrac23x + 2[/tex]
When graphing inequalities
If the inequality sign is < or > then the line of the graph should be dashed.
If the inequality sign is ≤ or ≥ then the line of the graph should be solid.
If y < (less than) then the shading is below the line.
If y > (more than) then the shading is above the line.
Therefore, as the inequality is y < the line should be dashed and the shading should be below the dashed line.
To plot the line, substitute x = 0 and x = 3 into the equation:
[tex]\sf \implies -\dfrac23(0) + 2=2[/tex]
[tex]\sf \implies -\dfrac23(3) + 2=0[/tex]
Therefore, plot points (0, 2) and (3, 0). Draw a dashed straight line through the points. Shade below the dashed line.
Tracy has 40 feet of material to make the perimeter of a rectangular sandbox for her little brother.
What rectangle with whole-number side lengths would give the sandbox with the greatest area?
Answers
Answer:
11 and 9
Step-by-step explanation:
With a width of 11 and a length of 9 the area of the rectangle would be
11 * 9 = 99
By adding 11 and 9, then mulitplying it by 2 we get the perimeter
11 + 9 = 20
20 * 2 = 40
Pls answerrrrrrrrrrrrrrrrrrrrrr
Answers
Answer:
13
Step-by-step explanation:
the two lines with y in them are the same length
6y = y+65
5y = 65
y = 13
The diagram represents the factorization of a2+8a+12.
A 2-column table with 2 rows. First column is labeled a with entries a squared, 2 a. Second column is question mark with entries 6 a, 12. First row is labeled a with entries a squared, 6 a. Second row is labeled 2 with entries 2 a, 12.
What is the missing number that will complete the factorization?
6
8
12
24
Answers
Answer:
The answer is 6
Step-by-step explanation:
Answer: 6
Step-by-step explanation: took the quiz
What are the domain and range of the function f(x) = 3x + 5
Answers
Step-by-step explanation:
Here,let x = 1,2,3 and 4
Then,
Domain =(1,2,3,4)
Again,
f(1)= 3*1 + 5
=3 + 5
=8
f(2)=3*2 + 5
=6 + 5
=11
f(3)=3*3 + 5
=9 + 5
=14
f(4)=3*4 + 5
=12 + 5
=17
Therefore, Range=(8,11,14,17)
7
.
Marisela wants to create a trophy in the shape of a rectangular
pyramid with volume 0.1875 cubic foot. Complete the descriptions
by writing in the missing measurements. 7.6.6
Design #1: pyramid height = 1.5 ft; base width = 0.75 ft;
Answers
Answer:
Volume of a rectangular pyramid:
[tex]V=\dfrac13lwh[/tex]
where:
[tex]V[/tex] = volume[tex]l[/tex] = length of base[tex]w[/tex] = width of base[tex]h[/tex] = heightGiven:
[tex]V[/tex] = 0.1875 ft³[tex]w[/tex] = 0.75 ft[tex]h[/tex] = 1.5 ftSubstitute given values into the formula and solve for [tex]l[/tex]:
[tex]\implies 0.1875=\dfrac13 \cdot l \cdot 0.75 \cdot 1.5[/tex]
[tex]\implies 0.1875=\dfrac{1.125}{3} l[/tex]
[tex]\implies 0.1875=0.375 l[/tex]
[tex]\implies l=\dfrac{0.1875}{0.375}[/tex]
[tex]\implies l=0.5[/tex]
Therefore, the base length is 0.5 ft
$8400 is deposited at an APR of 5%. How much interest has been accrued after 6 years ?
Answers
Answer:
$2,856.80
Step-by-step explanation:
The formula for the balance of an account earning interest compounded annually is ...
A = P(1 +r)^t . . . . where P is the principal invested at annual rate r for t years
__
Using the given values, we find the account balance to be ...
A = $8400(1 +0.05)^6 ≈ $11,256.80
The excess over the initial investment is the interest earned:
$11,256.80 -8,400 = $2,856.80
The account has accrued $2,856.80 in interest after 6 years.
_____
Additional comment
If the account earns simple interest, it is computed using ...
I = Prt = $8400(0.05)(6) = $2,520
Which of the following are composite numbers? Select ALL that apply. 4 9 15 3 5 answers.
Answers
Answer:
4 and 9
Step-by-step explanation:
Composite numbers are whole numbers that can have more than 2 factors.
When a is greater than one the parabola ___
Answers
Answer:
parabola is open upwards
What is the equation of the line that passes through the point(6,-2) And has an undefined slope
Answers
Answer:
X=6
Step-by-step explanation:
Please help me thank you so much!
Answers
Answer: the third one
Step-by-step explanation: how i know by guessing