Exercise 10.4.1: Bayes' Theorem - detecting a biased coin. About (a) Sally has two coins. The first coin is a fair coin and the second coin is biased. The biased coin comes up heads with probability .75 and tails with probability .25. She selects a coin at random and flips the coin ten times. The results of the coin flips are mutually independent. The result of the 10 flips is: T,T,H,T,H,T,T,T,H,T. What is the probability that she selected the biased coin

Answers

Answer 1

Answer:

0.026

Step-by-step explanation:

Given the result of 10 coin flips :

T,T,H,T,H,T,T,T,H,T

Number of Heads, H = 3

Number of tails, T = 7

Let :

B = biased coin

B' = non-biased coin

E = event

Probability that it is the biased coin:

P(E Given biased coin) / P(E Given biased coin) * P(E Given non-biased coin) * P(non-biased coin)

P(E|B)P(B) / (P(E|B)*P(B) + P(E|B')P(B')

([(0.75^3) * (0.25^7)] * 0.5) /([(0.75^3) * (0.25^7)] * 0.5) + (0.5^10) * 0.5

0.0000128746 / 0.00050115585

= 0.0263671875


Related Questions

A cylinder has volume 63 cm3. What is the volume of a cone with the same radius and height?

Answers

it's answer is

volume of a cone = 21

sarah walks 1/4 mile every 1/2 hour​

Answers

Answer:

To find ratio mph (miles PER hour), we can write the information given as a fraction. (The miles will go on top and the number of hours will go on the bottom).

1/2=.5 miles

1/4-.25 miles

So we have .5miles/.25 hours

From here, we can do 2 things: divide to get 2miles/hour or you can see that you can reduce the fraction (.5/2=.25 and .25/.25=1). So again we get 2/1 miles per hour OR 2 mph

Hope that helps,

Gracie

A school buys 1,950 pencils. The pencils are sold in boxes, with 30 pencils in each box. If each box costs $4.05, what is the total cost, in dollars, that the school will pay for the pencils?

Answers

The answer is
1950/30=65 boxes
Cost of 1 box is =4.05
The cost of 65 boxes=4*65=263.5

Determine the measures of the following; (SOMEONE PLS) :v

Answers

arc AC=27°

arc BD=33°

arc CB=120°

hope it helps you ❣❣

Mark me as brainliest

Segment JL has endpoints J(-3, -4) and L(7, 6). What are the coordinate of point K, so that point K is on line segment JL and JK = 3/5 JL. Explain.​

Answers

Answer:

K(3,2).

Step-by-step explanation:

We want to find a point K(x,y).

JK = 3/5 JL.

This means that:

[tex]K - J = \frac{3(L - J)}{5}[/tex]

We use this to find both the x-coordinate and the y-coordinate of K.

x-coordinate:

x-coordinate of J: -3

x-coordinate of L: 7

[tex]K - J = \frac{3(L - J)}{5}[/tex]

[tex]x - (-3) = \frac{3(7 - (-3))}{5}[/tex]

[tex]x + 3 = 6[/tex]

[tex]x = 3[/tex]

y-coordinate:

y-coordinate of J: -4

y-coordinate of L: 6

[tex]K - J = \frac{3(L - J)}{5}[/tex]

[tex]y - (-4) = \frac{3(6 - (-4))}{5}[/tex]

[tex]y + 4 = 6[/tex]

[tex]y = 2[/tex]

The point is K(3,2).

PLEASE HELP DUE IN 3 minutes

Answers

Answer:

41-50

Step-by-step explanation:

Answer: 41-50

Step-by-step explanation:

It is the lowest one so it occurred less frequently.

Hope this helps :)

3) Suppose you deposit $10,000 in a savings account that pays interest at an annual rate of 5%
compounded quarterly. How many years will it take for the balance in your savings account to reach
$12,000?

Answers

9514 1404 393

Answer:

  3.67 years

Step-by-step explanation:

The amount is found using the compound interest formula.

  A = P(1 +r/n)^(nt)

for principal P invested at annual rate r compounded n times per year for t years.

We can solve this for t:

  A/P = (1 +r/n)^(nt) . . . . divide by P

  log(A/P) = (nt)log(1 +r/n) . . . . take the logarithm

  t = log(A/P)/(n·log(1 +r/n)) . . . . divide by the coefficient of t

Filling in the given values, we find ...

  t = log(12000/10000)/(4·log(1 +0.05/4)) ≈ 3.6692

It will take about 3.67 years for the balance to reach $12,000.

Answer:

the answer is 3.67 years

The rectangular pyramid below has a height of 6 inches what is the volume of the pyramid? A. 18 cubic inches
B. 40 cubic inches
C. 120 cubic inches
D. 360 cubic inches

Answers

I think it’s D sorry if I’m wrong

The Volume of rectangular Pyramid whose height inches is 40 cubic inches.

What is the Volume of rectangular pyramid?

The volume of the rectangular pyramid is defined as the capacity of the rectangular pyramid. In geometry, a rectangular pyramid is a three-dimensional geometric shape that has a rectangular base and four triangular faces that are joined at a vertex.

Here, height of pyramid = 6 inches

base area = 4 X 5 = 20 sq. inches

Volume of rectangular pyramid = 1/3 × Base Area × height

                                                       = 1/3 X 20 X 6

                                                      = 120 / 3

                                                      = 40 cu. inches

Thus, the Volume of rectangular Pyramid whose height inches is 40 cubic inches.

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I really don't know how to solve this because when you plot points there's usually only 2 points to plot not 3.

Answers

Answer is: 16.58
Photo below
Good luck

Samantha wants to move into an apartment when she begins school in the fall. Right now she
has a job where she makes $250 a week working 20 hours and will be able to keep this job once
she begins school. Her parents have decided to put $500 a month in for extras that she might
need once she begins school. Although Samantha is very excited about moving into an
apartment, she wants your advice on where to begin preparing for her move. She wants to put
together a budget but has no idea where to begin.
Explain to Samantha how to set up her budget.
a
b. Once Samantha has a budget, what should she consider when determining if moving
out when she is beginning school is a good idea or not. Give specific reasons why this
might be a good or bad idea.

Answers

Answer:

she should set up a budget on how much she makes

Step-by-step explanation:

I love turtles and animals

I need help please and thank you

Answers

Answer:

7

Step-by-step explanation:

subtract 8 from both sides so you are left with 4m=28

then divide both side by 4 then you get m=7

Answer: It’s B

Step-by-step explanation: because 4 x 7 + 8 = 36.  Hope that helped :)

The credit scores of 35-year-olds applying for a mortgage at Ulysses Mortgage Associates are normally distributed with a mean of 600 and a standard deviation of 125. (a) Find the credit score that defines the upper 20 percent. (Use Excel or Appendix C to calculate the z-value. Round your final answer to 2 decimal places.) Credit score (b) Eighty-five percent of the customers will have a credit score higher than what value

Answers

Answer:

a) The credit score that defines the upper 20% is 705.

b) Eighty-five percent of the customers will have a credit score higher than 470.38.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Mean of 600 and a standard deviation of 125.

This means that [tex]\mu = 600, \sigma = 125[/tex]

(a) Find the credit score that defines the upper 20 percent.

This is the 100 - 20 = 80th percetile, which is X when Z has a pvalue of 0.8. So X when Z = 0.84.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]0.84 = \frac{X - 600}{125}[/tex]

[tex]X - 600 = 0.84*125[/tex]

[tex]X = 705[/tex]

The credit score that defines the upper 20% is 705.

(b) Eighty-five percent of the customers will have a credit score higher than what value?

This is the 100 - 85 = 15th percentile, which is X when Z has a pvalue of 0.15. So X when Z = -1.037.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.037 = \frac{X - 600}{125}[/tex]

[tex]X - 600 = -1.037*125[/tex]

[tex]X = 470.38[/tex]

Eighty-five percent of the customers will have a credit score higher than 470.38.

A triangle has an area of 37.5 inches the height of the triangle is 20 inches what is the length of the base of the triangle?​

Answers

Answer:

base = 3.75 inches

Step-by-step explanation:

37.5 = 20b/2

37.5 = 10b

b = 3.75


The equation, y = -3/2x + 15 represents the relationship between the amount of water left in the tub (in liters) y, and how much time has passed (in minutes) x. since Khloe starting draining the bath tub. What is the meaning of the value of 15 in this equation?

Answers

Answer:

is b or c I hope this help

Help please some one

Answers

Answer:

i dont know im just doing this for the points

Mason makes $20 for each time he mows. Which equation represents the money he makes, d, in dollars that mason makes after he mows n lawns?
A) d=20n
B) n=20d
C) d=20+n
D) n=20+d
Please help ASAP thank you

Answers

it’s A) d=20n
since you get $20 per lawn that he mows

A football player ran for 11 yards. how many inches did the football player run?

Answers

Answer: 396 inches

Step-by-step explanation:

Let's remember that for every yard there are 36 inches

there are 11 yards total

so we need to multiply 36 by 11

36x11

396 inches

Answer:

396 inches

Step-by-step explanation:

You multiply the number of inches for every yard (36) by the total number of yards

11*36=396

When a new drug is created, the pharmaceutical company must subject it to testing before receiving the necessary permission from the Food and Drug Administration (FDA) to market the drug. Suppose the null hypothesis is "the drug is unsafe." What is the Type II Error? ( Select the one, correct letter option below) :

Answers

Answer:

Not to conclude that the drug is safe, when, in fact, it is safe.

Step-by-step explanation:

A type ii error is an error that occurs in a hypothesis testing when a person goes ahead to accept a null hypothesis when it is actually false and should be rejected.

To continue, here are the hypothesis:

H0: the drug is unsafe

H1: drug is safe.

A type ii error was committed here because H0, which is the null was accepted and it was concluded that the drug was unsafe, When in fact it should have been rejected. The conclusion should have been that the drug was safe.

find the area of this polygon - PLZZZZZ HELP I WILL GIVE 30 points T^T

Answers

Answer:

82 m should be correct i hope

Step-by-step explanation:

How many cannonballs are there in the eighth figure

Answers

Answer:

36

Step-by-step explanation:

Element X is a radioactive isotope such that its mass decreases by 59% every day. If an experiment starts out with 390 grams of Element X, write a function to represent the mass of the sample after tt days, where the hourly rate of change can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of change per hour, to the nearest hundredth of a percent.

Answers

The function representing the mass of Element X after t days is [tex]{\text} M(t) = 390 * (0.41)^t[/tex], and the percentage rate of change per hour is 2.46%.

Given:

Initial mass = 390 grams

Rate of decay = 59% = 0.59

The general form of an exponential decay function is:

[tex]{\text}y = a (1 - r)^t[/tex]

So, the function to represent the mass of the sample after t days would be:

[tex]{\text} (t) = 390 * (1 - 0.59)^t[/tex]

Simplifying this equation gives

[tex]M(t) = 390 * (0.41)^t[/tex]

Now, the hourly rate of change is

Hourly rate of change = 0.59 / 24  

                                     = 0.024583

                                     = 2.46% per hour.

Therefore, the function is [tex]{\text} M(t) = 390 * (0.41)^t[/tex]and the rate of change is 2.46%.

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Lenny took three of his textbooks home one night. He wanted to find how much his backpack weighed.

Which of these units is MOST appropriate for measuring the weight of Lenny’s backpack?

Answers

Answer:

Pounds.

Step-by-step explanation:

Who in the holy dimension is gonna measure the weight of a bag in ounces and grams? Tons are just not even close to... Do you know how much a ton is? OHMY.

1 GRAM = 0.00220462 Pound

1 OUNCE = 0.0625 Pound

1 POUND = 16 Ounces

1 TON = 2000 Pounds

You wana carry a 2000 pound bag? I dont think so.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

GL :)

5th grade math. correct answer will be marked brainliest

Answers

Answer:

8 1/12 boxes

Step-by-step explanation:

Your first step to solve this problem is to convert those fractions to a common denominator. I would choose 12. So your first would be 4 4/12 and your second would be 3 9/12. You would then add those up and get 8 1/12 boxes of muffins bought at the bake sale.

please help!!!!! Its timed !!!!! Ill give out most brainly and extra points !!!

Answers

This is an Isoceles triangle. That means 180˚-50˚=130˚

130˚/2=65˚

Answer:

D) 65

Step-by-step explanation:

x + x + 50 = 180

2x + 50 = 180

2x = 130

x = 65

Question 3 Matt has yard of fishing line. He uses of the line to make fishing knots. How many yards of fishing line does Matt use to make fishing knots? Show your work Solution

Answers

Answer:

aSDFGHJLLMNNBBBBVCDDG

Step-by-step explanation:

Which statement is not true about the pattern shown?
2/3 4/6 8/12 16/24
A-Each fraction is greater than the previous fraction.
B-Each fraction is equal to the previous fraction in the pattern multiplied by
C-Each fraction is equivalent to 2/3
D-The next fraction in the pattern is 32/48

Answers

Answer:

The answer is A-Each fraction is greater than the previous fraction.

Step-by-step explanation:

To prove that A is wrong, first simply all fractions.

2/3 is already simplified.

4/6 can reduce to 2/3, which already proves that A is wrong.

So, because 2/3 and 4/6 are equal fractions, and A says that each fraction is greater than the previous one, A is wrong.

Find the volume of a pyramid with a square base, where the area of the base is
8.3 m² and the height of the pyramid iş 9.8 m. Round your answer to the nearest
tenth of a cubic meter.

Answers

Answer: 27.1 cubic meters

Step-by-step explanation: The area for finding the volume of a pyramid is V=1/3 Bh, where B= base, and h=height. To substitute in the numbers from the problem, you get V=1/3 times 8.3 times 9.8. 9.8 times 8.3 is 81.34. 81.34 times 1/3 rounds to 27.1.

Use the equation below to find y, if m=6, x=4, and b= 15. y=mx-b​

Answers

Answer:

9

Step-by-step explanation:

Y = MX-B,

therefore Y = (6*4) - 15,

so Y = 24 - 15

Y = 9

i
You are given the difference of the numbers of boys and girls in a class and the ratio of boys to girls. How many boys
and how many girls are in the class?
4 more girls; 9 for every 13
There are
boys and
girls in the class.

Answers

Answer:

Maybe they are all 13s th am sure

Write this equation in standard form y=3x+10

Answers

Answer:

to standard form

3x-y = -10

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