What is the probability that a fair die never comes up an even number when it is rolled six times? (note: enter the value of probability in decimal format and round it to three decimal places.)?

Answers

Answer 1

Let us compute first the probability of ending up an odd number when rolling a dice. A dice has faces with numbers 1 up to 6. The odd numbers within that is 3 (1, 3 and 5). Therefore, each dice has a probability of 3/6 or 1/2. Then, you use the repeated trials formula:

Probability = n!/r!(n-r)! * p^r * q^(n-r), where n is the number of tries (n=6), r is the number tries where you get an even number (r=0), p is the probability of having an even face and q is the probability of having an odd face.

Probability = 6!/0!(6!) * (1/2)^0 * (1/2)^6
Probability = 1/64

Therefore, the probability is 1/64 or 1.56%.

Related Questions

jim sold 200 litters of soda at baseball game.How much is this in milliters?

Answers

1 liter = 1000 milliliter

1000 * 200 = 200000

So, 200000 milliliter is the answer.

Answer: 200,000 ml of soda

One liter is 1000 milliliters. To convert between them, multiply 200 by 1000 to get 200,000

Of the books in a library, 1/3 came from Robbie's collection and 15 came from Marta's. Of the rest, 15 were Elena's 1/5 were Winfield's, and 5 were purchased from the bookstore. How many book are there in the library?

Answers

library amount: l
Robbie: r=(1/3)l
Martha: m=15
rest of books: l-r-m=e+w+b
Elena: e=15
Winfield: w=1/5(e+w+b)
bookstore: b=5

w=(e+w+b)/5
w=(15+5+w)/5
w=4+w/5
(4/5)w=4
w=5

l-r-m=e+w+b
l-(1/3)l-15=15+5+5
(2/3)l=25+15
(2/3)l=40
l=60=amount of books

The total number of books in the library are 75.

What is an equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.

What will be the equation for given scenario?

Let the total number of books in the library be x.

The equation formed by using given information will be [tex]\frac{x}{3} +15+15+\frac{x}{5}+ 5=x[/tex]

Collect the like terms,

[tex]\frac{x}{3} +35+\frac{x}{5}=x[/tex]

On solving the equation for x we get x=75.

Therefore, the total number of books in the library are 75.

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amy has 72 sweets in bag.she keeps 1/4 of them for herself,but shares the remainder between 6 of her friends.how many sweets will she give to each of her friends?

Answers

Amy keeps 18 sweets. find this by dividing 72 by 4

she has 54 left to share

54 divided by 6 is how many sweets each friend will get

Each friend gets 9 sweets

A ship traveled for a total of 72 miles over the course of 6 hours. Heading south, the ship traveled at an average speed of 13 miles per hour, and heading east, it traveled at an average speed of 10 miles per hour. For how many hours was the ahi heading east?

Answers

recall your d = rt, distance = rate * time

the rate going south is 13, the rate going east is 10

it took a total amount of 6hours and 72miles for the whole travel

so.. if going say hmmm South, it covered a distance of "d", then going East it covered a distance of the slack from 72 and "d", it covered "72 - d" miles

so, if going South it took "t" hours, then going East it took the slack from 6 and "t", or "6 - t" hours

thus [tex]\bf \begin{array}{lccclll} &distance&rate&time\\ &-----&-----&-----\\ South&d&13&t\\ East&72-d&10&6-t \end{array} \\\\\\ \begin{cases} \boxed{d}=13t\\ 72-d=10(6-t)\\ ----------\\ 72-\boxed{13t}=10(6-t) \end{cases}[/tex]

solve for "t"

so, it travelled East for 6-t hours

find the solution x-4y=9 and x-y=-9

Answers

see picture for solution

At the frozen yogurt shop, a machine fills cups with 4 ounces of frozen yogurt before the customer adds the toppings. After the cups are filled, customers add as many toppings as they want without the total weight exceeding 7 ounces. Which of the following graphs represents the acceptable weights for the frozen yogurt options?

Answers

The acceptable weight is within the range of [4, 7]

So the answer will be the 3rd graph

Answer: Third graph represents the acceptable weights for the frozen yogurt options.

Step-by-step explanation:

Since we have given that

Number of ounces of frozen yogurt a machine fills cups with before the customer adds the toppings = 4

After the cups are filled, customers add as many toppings as they want without the total weight exceeding 7 ounces.

So, it means the weight should be lie between 4 ounces and 7 ounces.

So, it can be written as [4,7].

4≤ x ≤7, here, x is the weight of frozen yogurt.

So, third graph represents the acceptable weights for the frozen yogurt options.

Gabrielle's age is three times Mikhail's age. The sum of their ages is 44. What is Mikhail's age?

Answers

g=gabby's age
m=micsdjfsdf's age

g=3m

sum is add
g+m=44

subsitute 3m for g
3m+m=44
4m=44
divide by 4 both sides
m=11

mikhail is 11 year old

Mikhail is 11 yrs old because 11 times 3 is 33. 33 plus 11 is 44

Need help with this word problem

Answers

check the picture below.

notice, we get -10 and 8, well, it cannot be a negative value, since it's the unit of a dimension.

so, the width is (1/2)x and the height is x+2.

The histogram shows the duration, in minutes, of movies in theaters.

What relationship between the median and mean is shown by the histogram?

A) The mean is less than the median.

B) The median is less than the mean.

C) The mean is equal to the median.

D) The median and mean cannot be compared from a histogram.

Answers

A histogram is a type of bar graph that presents the frequency of your data. In this problem, the histogram shows the frequency of movies (y-axis) with respect to the minutes of their duration (x-axis). Example, there are 2 movies that have a duration of 84-91 minutes, 4 movies having a duration of 91-98 minutes, and so on and so forth.

The mean of these data is (2+4+5+4+3+3+2+2)/8 = 3.125
The median is the middle data when the frequency is arranged from least to greatest. Thus, the median in the data set 2, 2, 2, 3, 3, 4, 4, 5 is 3. Therefore, the mean is greater than the median.

The answer is: the median is less than the mean

mean is equal to median.

Which quantity is proportional to 20/5?

Answers

Well can you be a little more specific? There's an infinite amount. For example, there's 4, 8/2, 12/3, 16/4, and you get the idea.

Can anyone help me solve a trigonomic identity problem and also help me how to do it step by step?

it's ((cos theta) * (cot theta))/(1-sin theta) - 1 = csc theta

Answers

[tex]\bf cot(\theta)=\cfrac{cos(\theta)}{sin(\theta)} \qquad csc(\theta)=\cfrac{1}{sin(\theta)} \\\\\\ sin^2(\theta)+cos^2(\theta)=1\\\\ -------------------------------\\\\[/tex]

[tex]\bf \cfrac{cos(\theta )cot(\theta )}{1-sin(\theta )}-1=csc(\theta )\\\\ -------------------------------\\\\ \cfrac{cos(\theta )\cdot \frac{cos(\theta )}{sin(\theta )}}{1-sin(\theta )}-1\implies \cfrac{\frac{cos^2(\theta )}{sin(\theta )}}{\frac{1-sin(\theta )}{1}}-1\implies \cfrac{cos^2(\theta )}{sin(\theta )}\cdot \cfrac{1}{1-sin(\theta )}-1 \\\\\\ \cfrac{cos^2(\theta )}{sin(\theta )[1-sin(\theta )]}-1\implies \cfrac{cos^2(\theta )-1[sin(\theta )[1-sin(\theta )]]}{sin(\theta )[1-sin(\theta )]}[/tex]

[tex]\bf \cfrac{cos^2(\theta )-1[sin(\theta )-sin^2(\theta )]}{sin(\theta )[1-sin(\theta )]}\implies \cfrac{cos^2(\theta )-sin(\theta )+sin^2(\theta )}{sin(\theta )[1-sin(\theta )]} \\\\\\ \cfrac{cos^2(\theta )+sin^2(\theta )-sin(\theta )}{sin(\theta )[1-sin(\theta )]}\implies \cfrac{\underline{1-sin(\theta )}}{sin(\theta )\underline{[1-sin(\theta )]}} \\\\\\ \cfrac{1}{sin(\theta )}\implies csc(\theta )[/tex]

You draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second. find the probability that the first card is an ace and that the second card is an ace?

Answers

4 aces in a deck

52 cards

you have a 4/52 reduced to 1/13 probability of picking an ace.

without replacing it there would be 51 cards left and 3 aces

so second probability of picking an ace is 3/51 reduced to 1/17

the probability of doing both = 1/13 x 1/17 = 1/221

Answer:

conf

Step-by-step explanation:

How many solutions to 15x+11=8x

Answers

To get the number of solutions in the equation given we shall be required to solve the equation;
15x+11=8x
collecting like terms we get:
11=8x-15x
11=-7x dividing both sides by -7 we get:
x=-7/11
therefore we conclude that the number of solutions is one

2/3 of a number is 32, what is the number?

Answers

2/3×a=32
a=32×3/2
a=96/2
a=48
The number is 48

2/3n = 32
Integers:- 3/2•2/3 = 32/1 = 3/2 = 96/2 = 48

True or false: the difference between the lower limit of a confidence interval and the point estimate used in constructing the confidence interval is called the sampling error.

Answers

Its true.
Sampling error is an error which is calculated by finding the difference between the lower limit or upper limit of a confidence interval and the point estimate used in constructing the confidence interval.
As we can calculate the difference, so sampling error can be positive or negative.

Explain how you can use place value patterns to describe how 50 and 5000 compare

Answers

The place value pattern is a system of patterns of tens in which every place value is ten times the value on its right. The place value pattern system is used to write numbers that are 10 times as much as or 1/10 of any given number.
The place values in the pattern are: ones, tens (10*ones), hundreds (10*tens), thousands (10*hundreds),...
So, 50 = 5 tens
5000= 5 thousands, 0 hundreds, 0 tens, 0 ones

So, 5000 > 50

A turkey was cooked at 300 f in the oven for 5 hours. the internal temperature rose from 35 f to 150 f. what was the average rise in temperature per hour

Answers

What do you think the answer is? Tell me and I will help you some more! :)

Which sentence best describes the independent and dependent variables in the following problem? The parking garage charges $3 for the first hour of parking and $1.45 for each additional hour.Which sentence best describes the independent and dependent variables in the following problem? The parking garage charges $3 for the first hour of parking and $1.45 for each additional hour.

Answers

The dependent variable is the additional charge applied for each hour whereas the independent variable is the charge to be applied on the first hour

The dependent variable would be $1.45 for each additional hour. The cost depends on every hour so we can't really calculate it unless we have the hours given.

$3 is independent since it's only charged on the first hour. It doesn't depend on any other information.

A home pregnancy test is not always accurate. suppose the probability that the test indicates that a woman is pregnant when she actually is not is 0.02, and the probability the test indicates that a woman is not pregnant when she really is, is 0.03. assume that the probability that a woman who takes the test is actually pregnant is 0.7. what is the probability that a woman is pregnant if the test yields a not pregnant result?

Answers

Set Events:
T=tests positive~T=tests negativeP=subject is pregnant~P=subject is not pregnant
We are givenP(T n ~P)=0.02P(~T n P)=0.03P(P)=0.7
recall by definition of conditional probabilityP(A|B)=P(A n B)/P(B)

Need to find P(P|~T)
First step: make a contingency diagram of probabilities (intersection, n)
P ~P sum
T 0.67 0.02 0.69=P(T)
~T 0.03 0.28 0.31=P(~T)
sum 0.70 0.30 1.00
=P(P) =P(~P)

therefore
P(P|~T)=P(P n ~T)/P(~T)=0.03/0.31 [ both read off the contingency table ]
=0.0968

Final answer:

The probability of a woman being pregnant if a home pregnancy test yields a negative result can be calculated using conditional probabilities and Bayes' theorem. From the provided probabilities, we can substitute into Bayes' theorem to calculate this probability.

Explanation:

The subject of this question is based on conditional probabilities. From the question we know that:

The probability of the test indicating a woman is pregnant when she's not (false positive) is 0.02 i.e., P(Positive|Not Pregnant) = 0.02 The probability of the test indicating a woman is not pregnant when she actually is (false negative) is 0.03 i.e., P(Negative|Pregnant) = 0.03 The probability that a woman who takes the test is actually pregnant is 0.7 i.e., P(Pregnant) = 0.7

From the above, we can find the probability of a woman being pregnant even though the test results are negative. To find this we need to use Bayes' theorem, which states:

P(A|B) = P(B|A) * P(A) / P(B)

So, to calculate the probability of a woman being pregnant given a negative test result P(Pregnant|Negative), we need the probability of getting a negative result when pregnant P(Negative|Pregnant), the probability of a woman actually being pregnant P(Pregnant), and the total probability of getting a negative test result P(Negative).

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Multiply and Dividing Rational Numbers

8/9 ÷ 2/3

7/8 × 1/4

3/4×1/6

Answers

essentially is just

[tex]\bf \cfrac{8}{9}\div \cfrac{2}{3}\implies \cfrac{8}{9}\cdot \cfrac{3}{2}\implies \cfrac{8\cdot 3}{9\cdot 2}\implies \cfrac{24}{18}\implies \cfrac{4}{3} \\\\\\ \cfrac{7}{8}\cdot \cfrac{1}{4}\implies \cfrac{7\cdot 1}{8\cdot 4}\implies \cfrac{7}{32} \\\\\\ \cfrac{3}{4}\cdot \cfrac{1}{6}\implies \cfrac{3\cdot 1}{4\cdot 6}\implies \cfrac{3}{24}\implies \cfrac{1}{8}[/tex]

Find the area of the shaded region below. The units are in feet.
Use 3.14 for π. Round your answer to two decimal places.

Answers

check the picture below.

so.. simply, get the area of the two circles, with radius of 4, we did that, and get the area of the larger circle with radius of 8, we did that.

now... keep in mind that, the area of the larger circle, includes the area of the two smaller circles, if you subtract the area of the two smaller circles from the larger's one, you're in effect making a hole in the larger circle, and what's leftover, is the shaded region.

Name the three different types of proof in math and give a description of each

Answers

I think the answer would be Paragraph Proof, The Flow Proof, and the Transformational proof. If you need the descriptions feel free to google it, or i can tell you that also!

If prices Increase at a monthly rate of 2.3%, by what percentage do they increase in a year?

Answers

In this question, the prices are Increased at a monthly rate of 2.3%. Since you are asked how much the percentage in a year and there is 12 month in a year, then you need to do the calculation 12 times.

The calculation would be (100%+2.3%)^12= 131.37344984%

That would be about 31.37% a year.

Find the area of sector AOB. Express your answer in terms of pi and rounded to the nearest tenth.

Answers

Final answer:

To find the area of sector AOB, use the formula A = (θ/360) * π * r^2, where θ is the angle of the sector in degrees and r is the radius. In this case, the angle θ is given as 1.11 and the radius is given as 4.5. Plugging these values into the formula, the area is approximately 0.139 m², rounded to the nearest tenth.

Explanation:

To find the area of sector AOB, we need to use the formula for the area of a sector: A = (θ/360) * π * r^2, where θ is the angle of the sector in degrees and r is the radius. In this case, the angle θ is given as 1.11 and the radius is given as 4.5. Plugging these values into the formula, we get A ≈ (1.11/360) * π * (4.5)^2.

Using a calculator, we can calculate the value to be approximately 0.139 m². Rounding to the nearest tenth, the area of sector AOB is 0.1 m².

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The areas of the sectors of circles 5 and 6 to the nearest tenth are 197.8 cm² and 6.3 ft² respectively.

What are the areas of the sectors?

The area of the sector of a circle can be expressed as:

Area = ( θ/360º ) × πr²

Where θ is the sector angle in degrees, R is the radius of the circle, and π is constant pi.

For question5)

Angle θ = 70 degrees

Radius r = 18 cm

Area =?

Area = ( θ/360º ) × πr²

Plug in the values:

Area = ( 70/360º ) × π × 18²

Area = 63π cm²

Area = 197.8 cm²

For question 6)

Angle θ = 180 degrees

Diameter d = 4ft

Radius r = 4/2 = 2ft

Area =?

Area = ( θ/360º ) × πr²

Plug in the values:

Area = ( 180/360º ) × π × 2²

Area = 2π ft²

Area = 6.3 ft²

Therefore, the area of the sector is 6.3 ft².

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what is 475% of 9.2?

Answers

To find this, multiply 9.2 by the decimal form of the percent (4.75). The answer is 43.7

475% of 9.2 is =43.7

Find the area under the standard normal curve between z = −2.57 and z = 1.27. Round your answer to four decimal places, if necessary.

Answers

P(-2.57 ≤ Z ≤ 1.27) = P(Z ≤ 1.27) - P(Z ≤ -2.57)

P(Z ≤ 1.27) = 0.8980
P(Z ≤ -2.57) = 1 - P(Z ≤ 2.57) = 1 - 0.99488 = 0.00512

P(-2.57 ≤ Z ≤ 1.27) = 0.8980 - 0.00512 = 0.89288
0.8929 (4 d.p.)

The area under the standard normal curve between z = −2.57 and z = 1.27 is, 0.8929

What is meant by Probability?

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

We have to give that,

To find the area under the standard normal curve between z = −2.57 and z = 1.27.

Now, the area under the standard normal curve is between z = −2.57 and z = 1.27 is,

P(-2.57 ≤ Z ≤ 1.27) = P(Z ≤ 1.27) - P(Z ≤ -2.57)

Since, P(Z ≤ 1.27) = 0.8980

And, P(Z ≤ -2.57) = 1 - P(Z ≤ 2.57)

= 1 - 0.99488

= 0.00512

Hence,

P(-2.57 ≤ Z ≤ 1.27) = 0.8980 - 0.00512

= 0.89288

= 0.8929

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PLEASE HELP WITH SOME GEOMETRY
Prove the following statement by contradiction using an indirect proof. In a triangle angle A = 90°, then the triangle is a right triangle. Which of the following choices would be the first step to temporarily assume?
angle A = 90°
the triangle is a right triangle
the triangle is not a right triangle
angle A is not 90°

Answers

The contradiction proof should start with a negation:
"The triangle is not a right triangle angle and A is not 90°"
Then you proof that this statement is false

The points A(12,7)A12,7, B(12,-3)B12,-3, C(-2,-3)C-2,-3, and D(-2,7)D-2,7 form rectangle ABCDABCD. Which point is halfway between AA and BB?

Answers

To find the midpoint of line segment AB, we find the total distance for both x and y coordinates and then divide each answer by 2.

A (12, 7)
B (12, -3)

Mid point ([tex] \frac{12+12}{2} [/tex], [tex] \frac{7+-3}{2} [/tex])
Mid point ([tex] \frac{24}{2} [/tex], [tex] \frac{4}{2} [/tex]}
Mid point (12, 2)

An apple farmer has planted 0.3 of his orchard with cherry trees. The orchard is 8.59 acres in size. How many acres are planted with cherry trees

Answers

0.3(8.59) = 2.577 rounds to 2.58 acres

A company uses a variable percentage markup of 35% .if the total cost of a product is $15,what is its selling price

Answers

Final answer:

The selling price of a product with a 35% markup on a cost of $15 is calculated by adding the markup amount of $5.25 to the cost, resulting in a selling price of $20.25.

Explanation:

To calculate the selling price of a product using a variable percentage markup, you first need to determine the amount of markup by converting the percentage to a decimal and multiplying by the cost of the product. In this case, with a 35% markup on a product that costs $15, the calculation is as follows:

$15 × 0.35 = $5.25

This $5.25 represents the amount of markup on the product. To find the selling price, you simply add the markup to the cost:

$15 + $5.25 = $20.25

Therefore, the selling price of the product would be $20.25.

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