If a fair coin is tossed 6 times, what is the probability, rounded to the nearest thousandth, of getting at most 2 heads?​

Answers

Answer 1

Answer:

[tex] \displaystyle 0.344[/tex]

Step-by-step explanation:

we are given that a coin is tossed 6 times and we want to find the probability of getting at most 2 heads.

To solve this problem,we can consider binomial distribution, which is given by

[tex] \displaystyle P(X = r) = \binom{n}{r} {p}^{r} {q}^{n - r} [/tex]

where:

P = binomial probabilityr = number of times for a specific outcome within n trials[tex]{n \choose r}[/tex] = number of combinationsp = probability of success on a single trialq = probability of failure on a single trialn = number of trials

we want to figure out the probability of getting at most 2 heads out of 6 trials , The probability can therefore be found by adding up all the binomial distributions including X=2 and less than it, Thus

[tex] \displaystyle P(X \leq 2) = P(X=0)+P(X=1)+P(X=2) [/tex]

[tex] \displaystyle P(X \leq 2) = \binom{6}{0} {p}^{0} {q}^{6 - 0} + \binom{6}{1} {p}^{1} {q}^{6- 1} + \binom{6}{2} {p}^{2} {q}^{6 - 2} [/tex]

when a coin is tossed, the probability of getting both head (success) and tail (failure) are ½ which is why ,the variables, p and q are assigned to ½. therefore substitute

[tex] \rm\displaystyle P(X \leq 2) = \binom{6}{0} { \left( \frac{1}{2} \right) }^{0} { \bigg( \frac{1}{2} \bigg) }^{ 6- 0} + \binom{6}{1} { \bigg( \frac{1}{2} \bigg) }^{1} { \bigg( \frac{1}{2} \bigg) }^{6 - 1} + \binom{6}{2} { \bigg( \frac{1}{2} \bigg)}^{2} { \bigg( \frac{1}{2} \bigg) }^{6- 2} [/tex]

since p and q are the same. it won't make any difference to write all the product of p and q as (½)⁶:

[tex]\rm\displaystyle P(X \leq 2) = \binom{6}{0} { \bigg( \frac{1}{2} \bigg) }^{ 6} + \binom{6}{1} { \bigg( \frac{1}{2} \bigg) }^{6} + \binom{6}{2} { \bigg( \frac{1}{2} \bigg) }^{6}[/tex]

In the expression the term (½)⁶ is common thus factor it out:

[tex]\rm\displaystyle P(X \leq 2) = { \bigg(\frac{1}{2}\bigg) }^{ 6} \left( \binom{6}{0} + \binom{6}{1} + \binom{6}{2} \right) [/tex]

calculate the combinations:

[tex]\rm\displaystyle P(X \leq 2) = { \bigg(\frac{1}{2}\bigg) }^{ 6} \left(1+6+15\right) [/tex]

simplify addition:

[tex]\rm\displaystyle P(X \leq 2) = { \bigg(\frac{1}{2}\bigg) }^{ 6} \left(22\right) [/tex]

simplify exponent:

[tex]\rm\displaystyle P(X \leq 2) = { \bigg(\frac{1}{64}\bigg) } \left(22\right) [/tex]

simplify multiplication:

[tex]\rm\displaystyle P(X \leq 2) = \frac{22}{64} [/tex]

dividing yields:

[tex]\rm\displaystyle P(X \leq 2) = 0.34375 [/tex]

[tex]\rm\displaystyle P(X \leq 2) \approx 0.344 [/tex]

In conclusion

The answer is 0.344


Related Questions

PLEASE HELP!!!!!! Im being timed

Answers

Answer:

9,6 hope this helps

9,6 I think so??????????

9. El radio de una pelota de básquetbol es aproximadamente 3.6 veces mayor
que el radio de una pelota de tenis. ¿Cuántas veces mayor es el volumen
de una pelota de básquetbol que el volumen de una pelota de tenis?
4
Nota: El volumen de una esfera es V = -tr

Answers

Answer:

so the volume of the basketball is 46.656 times greater than the volume of the tennis ball.

Step-by-step explanation:

−1 4/5−(−2 7/8)

4 3/4−(−1 1/12)

−1 4/5−(−2 7/8)

3 1/3-5

−1/3−(−1/2

Answers

Answer:

1) 43/40

2) 35/6

3) 43/40

4) -5/3

5) 1/6

Step-by-step explanation:

1)  -1 4/5 = -(1*5 +4)/ 5= -9/5

or          1= 5/5  so -1 4/5= -( 5/5+ 4/5)=-9/5

-2 7/8= -(2*8+7)/8=-23/8

=> -9/5 - ( -23/8)= -9/5 + 23/8 = (( -9*8)+(23*5))/40= (-72+ 115)/40

                                                                                =  43/40

2) 4 3/4= (4*4+3)/4= 19/4

-1 1/12= -(1*12+1)/12= -13/12

=> 19/4 - (-13/12)= 19/4 + 13/12 = ((19*3)+13)/12= (57+13)/12= 35/6

3) same like 1)

4) 3 1/3 = (3*3+1)/3= 10/3

=> 10/3 -5= (10- 3*5)/3= (10-15)/3= -5/3

5) -1/3 + 1/2= ((-1*2)+(1*3))/6 = (-2+3)/6= 1/6

What’s the answer???

Answers

Answer:

Step-by-step explanation:

PLZZZZ help it will mean a lot :)

Answers

3x = 18

Divide both sides by 3 and simplify

x=6

Answer:

Step-by-step explanation:

assuming  that you need to find the value of x

3x = 18

-divide both sides by 3

3x/3 = 18/3

-use the facts that 3/3 =1 and 18/3 = 3*6/3 = 6

x = 6

Anyone know the answers 11 through 14?Please help me.I’m tired

Answers

Answer:

11. [tex]x^{5}[/tex]

12. 5*[tex]x^{2}[/tex]

13. x+21

14. 2x-8

Step-by-step explanation:

(1/2)^x=2^-x could anyone tell me why​

Answers

Answer:

Anything to a negative power is always the reciprocal. An example might be 2⁻² can be written as 1/4

Step-by-step explanation:

Donna cut a wire into 7 equal pieces. The wire was originally 9.52 meters long. How long is each piece?

Answers

Answer:

1.36

Step-by-step explanation:

9.52/7

1.36 is the length of one of the 7 equal pieces

Practice
1. Hyatt Home Improvement uses H-shaped tile Design 1 Design 2
Design 3
designs on their buildings, advertisements, and
vehicles. The designs they use follow a specific
pattern. The first three designs are shown.
a. Describe the pattern in the designs.
b. Write two different expressions to represent
the number of tiles used in Design n. Use
algebraic properties to prove the two expressions are equivalent.
c. Explain how you could use technology to prove the two expressions in part (b)
are equivalent.
d. Create a table that displays the number of tiles used in each of the first 6 designs.
e. Create a graph of the data points in your table on the coordinate plane shown. Draw a smooth
curve to connect the points.
f. Do all of the points on the smooth curve make sense in terms of the problem situation? Explain
your reasoning.
g. Describe the pattern as linear, exponential, quadratic, or none of these. Explain your reasoning.
h. The owner of Hyatt Home Improvement wants to put one of their designs on an empty
rectangular sign in front of their headquarters. The empty sign is 10 feet tall and 12 feet wide. If he

Answers

Patterns are set of rules that guide the creation of a dataset. The observation from the first three designs are as follows:

The pattern is that the number of tiles increases as the design number increasesThe expressions for the number of tiles are [tex]n^2 + 2(n + 2)[/tex] and [tex]n^2 + 2n + 4[/tex]The expression can be proved to be equivalent using graph technology The points on the curve make sense in this scenario because all values are positiveThe pattern is quadratic.The largest design number that can enter an empty 10 by 12 ft sign is design number 8

The pattern

The first three design show that, as the design number increases (i.e. 1, 2, 3), the number of tiles used also increases (i.e. 7, 12, 19)

The expressions for the number of tiles

The design number and the number of tiles is represented as follows

[tex]1 \to 7[/tex]

[tex]2 \to 12[/tex]

[tex]3 \to 19[/tex]

From the designs, we observe that some tiles are at the middle, while other tiles are at the sides.

Design 1 has 1 tile at the center and 6 tiles at either sides.

So, we have:

[tex]1 \to 1 + 6[/tex]

[tex]2 \to 4 + 8[/tex]

[tex]3 \to 9 + 10[/tex]

Expand

[tex]1 \to 1^2 + 6 \to 1^2 + 2 \times 3 \to 1^2 + 2 \times (1 + 2)[/tex]

[tex]2 \to 2^2 + 8 \to 2^2 + 2 \times 4 \to 2^2 + 2 \times (2 + 2)[/tex]

[tex]3 \to 3^2 + 10 \to 3^2 + 2 \times 5 \to 3^2 + 2 \times (3 + 2)[/tex]

Notice the pattern,

The number of tiles in design n will be:

[tex]Tiles = n^2 + 2 \times (n + 2)[/tex]

Open bracket

[tex]Tiles = n^2 + 2n + 4[/tex]

Hence, the expressions for number of tiles in design n are:

[tex]n^2 + 2(n + 2)[/tex] and [tex]n^2 + 2n + 4[/tex]

Technology to prove that both expressions are equivalent

To prove that [tex]n^2 + 2(n + 2)[/tex] and [tex]n^2 + 2n + 4[/tex] are equivalent using technology, the graphs of [tex]n^2 + 2(n + 2)[/tex] and [tex]n^2 + 2n + 4[/tex] can be plotted and then compared

The table and graph for the first 6 designs

The table entry for the first 6 designs is calculated as follows:

[tex]n = 1\ \ \ \ \ Tiles = 1^2 + 2 \times 1 + 4 = 7[/tex]        

[tex]n = 2\ \ \ \ \ Tiles = 2^2 + 2 \times 2 + 4 = 12[/tex]        

[tex]n = 3\ \ \ \ \ Tiles = 3^2 + 2 \times 3 + 4 = 19[/tex]        

[tex]n = 4\ \ \ \ \ Tiles = 4^2 + 2 \times 4 + 4 = 28[/tex]        

[tex]n = 5\ \ \ \ \ Tiles = 5^2 + 2 \times 5 + 4 = 39[/tex]        

[tex]n = 6\ \ \ \ \ Tiles = 6^2 + 2 \times 6 + 4 = 52[/tex]        

So, we have:

[tex]\begin{array}{cc}Design & {Tiles} & {1} & {7} & {2} & {12} & 3 & {19} & {4} & {28} & {5} & {39}& {6} & {52} \ \end{array}[/tex]

See attachment for the graph of the above table

All the points on the curve make sense in this scenario because all values are positive.

The pattern type

We have:

[tex]Tiles = n^2 + 2n + 4[/tex]

When an equation has a degree of 2, the equation is quadratic.

Hence, the pattern is quadratic.

The largest design that an empty sign of 10ft by 12ft can contain.

From the first three designs:

The number of tiles on a complete row and column are always the same.

Design 1 has 3 tiles in its complete row and column

Design 2 has 4 tiles in its complete row and column

Design 3 has 5 tiles in its complete row and column

The relationship between the design number (d) and the number of complete tiles (t) is:

[tex]d = t - 2[/tex]

For the 10ft by 12ft empty sign

[tex]t = 10[/tex] because [tex]10 < 12[/tex]

So, we have:

[tex]d = t - 2[/tex]

[tex]d = 10 - 2[/tex]

[tex]d = 8[/tex]

Hence, the largest design number is design 8

Read more about patterns at:

https://brainly.com/question/13382968

5. After paying a tax of 8 palsa per rupee a man saves Rs. 18,400 per month Then his monthly income is 2 Points) 20,000​

Answers

Answer:

92% of Income is  Rs 18400

Step-by-step explanation:

I = 18400/.92 = Rs 20000

1. Your school's Key Club decided to sell fruit baskets to raise
money for a local charity. The club sold a total of 80 fruit
baskets. There were three different types of fruit baskets.
Small fruit baskets sold for $15.75 each, medium fruit baskets
sold for $25 each, and large fruit baskets sold for $32.50
each. The Key Club took in a total of 52086.25. and they sold
twice as many large baskets as small baskets.
a. Formulate a system of three linear equations in three
variables to represent this problem situation. Be sure to
define your variables.
b. Solve the system of three linear equations using
technology with matrices. Write your answer in terms of
the problem situation.
c. Describe the solution in terms of the problem situation.
2. Is it always easier to solve a system of linear equations using
matrices? Explain your reasoning.

Answers

Let the small , medium and large baskets be denoted by s,m & l

Formulating the equations

s+m+l= 80--------- equation1

$15.75s+ $25 m + $32.5l = $2086.25------equation2

2s=l---------equation 3

Using the technology  s=15, m=35 and l= 30

15+35+30= 80--------- equation1

$15.75(15)+ $25 (35)+ $32.5 (30) = $2086.25------equation2

2(15)=(30)---------equation 3

Yes because multiple variables can be easily calculated through matrices using technology

In Matrix form

[tex]\left[\begin{array}{ccc}1&1&1\\15.75&25&32.5\\-2&0&1\end{array}\right][/tex] [tex]\left[\begin{array}{c}s\\m\\l\end{array}\right][/tex]     = [tex]\left[\begin{array}{c} 80\\2086.25\\0\end{array}\right][/tex]

Let A= [tex]\left[\begin{array}{ccc}1&1&1\\15.75&25&32.5\\-2&0&1\end{array}\right][/tex]

Z= [tex]\left[\begin{array}{c}s\\m\\l\end{array}\right][/tex]    

B = [tex]\left[\begin{array}{c} 80\\2086.25\\0\end{array}\right][/tex]

Z= A⁻¹ B

A⁻¹= A mod/ det A

det A= -1

Using the technology  s=15, m=35 and l= 30

15 small baskets,

35 medium baskets

30 large baskets were sold.

Part C:

15+35+30= 80--------- equation1

$15.75(15)+ $25 (35)+ $32.5 (30) = $2086.25------equation2

236.25+ 875+ 975=$2086.25

$2086.25=$2086.25

2(15)=(30)---------equation 3

Answer 2:

Yes because multiple variables can be easily calculated using technology.

N.B There is a typing error in question its $2086.25 not 52086.25

factors of 15,17 ,26 & 80​

Answers

Answer:

Factors of 15: 1, 3, 5 and 15.

Factors of 17: 1 and 17.

Factors of 26: 1, 2, 13 and 26

Factors of 80: 1, 2, 4, 8, 10, 20, 40, and 80.

Actually you can find all the answers in the Internet.

Solve for x: 4x + 1/2 (2x + 4) > 12
( 9th grade Algebra 1)

Answers

Answer:

x > 2

Step-by-step explanation:

Distribute and cross-simplify 1/2 with parenthesis

4x + x + 2 > 12

Solve left side

5x + 2 > 12

Subtract 2 from both sides

5x > 10

Divide both sides by 5

x > 2

Someone answer this

Answers

Answer:

1st box is "a 90°clockwise rotation about the origin

2nd box is "a 180° rotation about the origin

3rd box is "a 90° counterclockwise rotation about the origin

[tex]\frac{7}{8} + \frac{3}{4}[/tex]

Answers

Answer:

Step-by-step explanation:

7/8 + 3/4

7/8 + 6/8

13/8 = 1 5/8

Please help ASAP 17x - 4(4x - 3)

Answers

Step-by-step explanation:

17x-4(4x-4)

17x-16x+8

X+8

Answer:

x + 12

Step-by-step explanation:

17x - 4(4x - 3)

17x - 16x + 12

x + 12

hewo um what is 1804 divided by 12 and has anyone seen my hacker friend.

Answers

Answer:

150.333

Step-by-step explanation:

The three is repeated

a triangle has a width of 4 cm and perimeter of 26 cm. find the length​

Answers

Answer:

9 ufh fcnbscbhbvxdfhbbhukkkocd

I needddddd heelllpppp pleaseeee

Answers

Answer:

3/2

Step-by-step explanation:

Csc(theta) = 1/Sin(theta)

So we have to find the side opposite theta.

a = 3*sqrt(5)

b = ?

c = 9

a^2 + b^2 = c^2

(3sqrt(5)) ^2 + b^2 = 9^2

9*5 + b^2 = 81

b^2 = 81 = 45

b^2 = 36

sqrt(b^2) = sqrt(36)

b = 6

Sin(theta) = 6/9

Csc(theta) = 1 / sin(theta) = 9/6

Csc(theta = 3/2

Problem 3

Answer:   3/2

=====================================================

Explanation:

Use the pythagorean theorem to find the length of the missing side.

[tex]a^2 + b^2 = c^2\\\\a^2 + (3\sqrt{5})^2 = 9^2\\\\a^2+3^2*(\sqrt{5})^2 = 9^2\\\\a^2 + 9(5) = 81\\\\a^2 + 45 = 81\\\\a^2 = 81-45\\\\a^2 = 36\\\\a = \sqrt{36}\\\\a = 6\\\\[/tex]

This is the length of the missing vertical side. This side is opposite the angle theta.

[tex]\csc = \text{cosecant}\\\\\csc(\theta) = \frac{\text{hypotenuse}}{\text{opposite}}\\\\\csc(\theta) = \frac{9}{6}\\\\\csc(\theta) = \frac{3*3}{3*2}\\\\\csc(\theta) = \frac{3}{2}\\\\[/tex]

Alternatively, you can compute it like this

[tex]\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\\sin(\theta) = \frac{6}{9}\\\\\sin(\theta) = \frac{2}{3}\\\\\csc(\theta) = \frac{1}{\sin(\theta)}\\\\\csc(\theta) = 1 \div \sin(\theta)\\\\\csc(\theta) = 1 \div \frac{2}{3}\\\\\csc(\theta) = \frac{3}{2}\\\\[/tex]

30, 32, and 34 Please! I WILL GIVE BRAINLIEST

Answers

Answer:

see explanation

Step-by-step explanation:

Since AL bisects ∠ KAT then ∠ 1 = ∠ 2

(30)

7x + 3 = 6x + 7 ( subtract 6x from both sides )

x + 3 = 7 ( subtract 3 from both sides )

x = 4

(32)

SAT is a straight line , then

∠ 1 + ∠ 2 + ∠ 3 = 180° , then

x + x + 4x = 180

6x = 180 ( divide both sides by 6 )

x = 30

(34)

Similar to (32)

x + 12 + x + 12 + 6x - 20 = 180 , that is

8x + 4 = 180 ( subtract 4 from both sides )

8x = 176 ( divide both sides by 8 )

x = 22

Answer:

30) x= 4

32) x=30

33) x=22

Step-by-step explanation:

All step by step explainations are in pic below

Select all the expressions that are equivalent to 3^2 · 3 ^(-6)

Answers

Answer:

[tex] {3}^{2} \times {3}^{ - 6} \\ = {3}^{2 + ( - 6)} \\ = {3}^{2 - 6} \\ = {3}^{ - 4} [/tex]

Simplify the answer has to be a positive exponent Please help!

Answers

5^4 /5

Use the exponent rule x^a/x^b = x^a-b

5^4/5 = 5^4-1 = 5^3

Answer as a positive exponent is 5^3

where can i find the answers?

Answers

Answer:

I don't know where can you find this question's answer.

a + 1 = 3000
a = ?

This is my first question, I know the answer. I just wanna test the platform.

Answers

Answer:

2999

Step-by-step explanation:

a + 1 = 3000

=> Subtracting 1 from both sides,

=> a + 1 - 1 = 3000 - 1

=> a = 2999

Which expressions are equivalent

Answers

Answer:

The choose B. 2(2m-1)-8m

Step-by-step explanation:

2(2m-1)-8m = 4m-2 + (-8m)

I hope I helped you^_^

i need some help!!!!!!!!!!!!!!!!!!!!!!!

Answers

Step-by-step explanation:

We are dealing with theoretical probability. This means that our probability of said outcome is

[tex] \frac{x}{y} [/tex]

where x is the outcome we want, and y is the total number of outcomes possible.

28. There is 3 triangles out of 6 polygons so the probability is 1/2.

29.There is 1 Pentagon so the probability is 1/6.

30. This is a complement to question 28. A complement is the inverse of the problem. A complement and its original add to 1 so the probability of both getting a triangle is 1/2.

31. There is 4 non quadraletrial so the probability is 2/3.

32. There is 3 figures that has more sides than three so 1/2 is the probability.

33.There is only multi right angles figures so 1/2 is the probability.

34. There is 30 days in April so the probability it's the 29th is

[tex] \frac{1}{30} [/tex]

35. There is 31 days in July and 15 days after the 16th. So the probability

is

[tex] \frac{15}{31} [/tex]

1. Which of the following is an example of like
terms?
a. - 16 and - 16x
b. x and x2
C, 50y and y
d. 20a and 2

Answers

the answer shoupd be c

The value of tan1°tan2ºtan3⁰ (a) 0 (b)-1 (c) 1 (d) 2 tan890 is equal to​

Answers

Step-by-step explanation:

Answer-

b) 1




what is the purpose?

[tex] \\ [/tex]

Answers

TeX was designed with two main goals in mind: to allow anybody to produce high-quality books with minimal effort, and to provide a system that would give exactly the same results on all computers, at any point in time (together with the Metafont language for font description and the Computer Modern family of typefaces) ...

Answer:

I hope it will helpful.

Step-by-step explanation:

I hope it will help you.

a region's average movie theater ticket price in 2007 was $6.72. For 2017, it was estimated to be $8.81. Find the percent of increase in average movie theater ticket price for this 10-year periods

Answers

Answer:

31.1011905%

Step-by-step explanation:

Take the new price and subtract the original price

8.81 - 6.72

2.09

Divide by the original price

2.09/6.72

.311011905

Change to percent form

31.1011905%

Percent of increase in average movie theatre ticket price will be 31.1%

    Given prices of the ticket in two different years are,

In year 2007 price of the ticket was $6.72After 10 years price of the ticket is $8.81

To calculate the percent increase in the price of an object expression to be used,

Percent increase = [tex]\frac{\text{Final price - Initial price}}{\text{Initial price}}\times 100[/tex]

                             = [tex]\frac{8.81-6.72}{6.72}\times 100[/tex]

                             = [tex]0.311\times 100[/tex]

                             = [tex]31.10[/tex]%

          Therefore, percent of increase in the price of the ticket will be 31.1%

Learn more,

https://brainly.com/question/11265758

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