Exercise 12.1.1: Coin flips and events. About A coin is flipped four times. For each of the events described below, express the event as a set in roster notation. Each outcome is written as a string of length 4 from {H, T}, such as HHTH. Assuming the coin is a fair coin, give the probability of each event. (a) The first and last flips come up heads. (b) There are at least two consecutive flips that come up heads. (c) The first flip comes up tails and there are at least two consecutive flips that come up heads.

Answers

Answer 1

Answer:

a [tex]Pr = 0.25[/tex]

b [tex]Pr = 0.50[/tex]

c [tex]Pr = 0.1875[/tex]

Step-by-step explanation:

Given

[tex]n = 4[/tex] --- number of times

[tex]r = 2[/tex] --- faces of a coin

First, is to determine the sample size.

This is calculated as:

[tex]Size =r^n[/tex]

[tex]Size =2^4[/tex]

[tex]Size =16[/tex]

Solving (a): First and last slip is head

This event is represented as:

[tex]E=\{HHHH, HHTH, HTHH, HTTH\}[/tex]

The probability is calculated as:

[tex]Pr = \frac{n(E)}{Size}[/tex]

[tex]Pr = \frac{4}{16}[/tex]

[tex]Pr = 0.25[/tex]

b) At least 2 consecutive flips that is heads.

This event is represented as:

[tex]E=\{HHHH,HHHT,HHTH,HHTT,THHH,THHT,HTHH,TTHH\}[/tex]

The probability is calculated as:

[tex]Pr = \frac{n(E)}{Size}[/tex]

[tex]Pr = \frac{8}{16}[/tex]

[tex]Pr = 0.50[/tex]

 

c) First is tail and at least 2 consecutive flips is head.

This event is represented as:

[tex]E=\{THHH,THHT,TTHH\}[/tex]

The probability is calculated as:

[tex]Pr = \frac{n(E)}{Size}[/tex]

[tex]Pr = \frac{3}{16}[/tex]

[tex]Pr = 0.1875[/tex]  


Related Questions

A=53sq.in find the value of x. Round to the nearest tenth

Answers

Answer:

shawty i think we need more info to solve this-

Step-by-step explanation:

Consider the function f(x) = 2 + 2x - 15. What are the x-intercepts of the function?

Answers

Answer:

x=6.5

Step-by-step explanation:

I got the x- intercept as 6.5 because I found the x value when y equals 0.

0=2+2x-15

Next, I added 2+-15 and got -13.

0=2x-13

Then, I added 13 to both sides so that I could have x by itself.

13=2x

Next, I divided 2 on both sides so I could find the value of x.

6.5= x

In conclusion, the x- intercept of f(x)=2+2x-15 is 6.5.  

Find the upper quartile of the given data: ​ ​ 31 , 47 , 88 , 92 , 92

Answers

Answer:

92 is the answer

Step-by-step explanation:

PLEASE HELP !! ILL GIVE BRAINLIEST !!

Answers

Answer:

angle klj and angle poq :)

Step-by-step explanation:

Find two ratios equivalent to each ratio 3:11

Answers

Answer:

Multiplying each side by 5⇒ 15: 55

Multiplying each side by 10⇒30:110

Step-by-step explanation:

Answer:  3:11= 30:110 and 6:22

Step-by-step explanation:

30:110 is multipled by 10 and 6:22 is multiplied by 2!

It can be divided or multiplied by whatever number you want! If you want to divide it by one number, make sure that it will be without the remainder because it’s equivalent! I hope I helped you!

5m²+15m=0

t²-5t+6=0

5p²+12p+4=0

2a²+10a-48=0

x(2x+5)=0

Answers

Answer:

m=1, m= -3

t=3, t=2

p= -0.4, p= -2

a= 3, a= -8

x=0, x= -2.5

Answer:

I hope this helps a little bit.

It Is Not Fake

It Got Answers Promise

find the length of the missing side.

Answers

Answer:

I believe it is 12

Step-by-step explanation:

but I am not 100 percent sure

May someone pls explain how to do this?

Question: In the image below, the measure of angle 2 is 75°. Find the measures of angles 1, 3, 4, 5, 6, 7, and 8.

Answers

Answer:

1=105

3=105

4=75

5=105

6=75

7=105

8=75

Step-by-step explanation:

angles 1 and 2 are supplementary, this means that the sum of the two angles equals 180(they make a straight line).

This means that the cross of the two lines(p and m) will cause angles 1 and 3 to be the same (2 and 4 will also be the same).

lines m and n are parallel, which means that angles 1,2,3, and 4 will be that same as their corresponding angle in angles 5,6,7, and 8.

I hope that made sense.

A shirt is on sale for 35% off the original price. If the original price is $39.00 what is the sale price?

Answers

Answer:

$25.35

Step-by-step explanation:

You just take off the percentage from the original price to get your final answer.

Hope this helps c:

. Dinah bought 3 packages of ground beef. The packages weigh 3 3/4 pounds, 1 1/8 pounds, and 2 1/2 pounds. How many pounds of ground beef did Dinah buy

Answers

Answer:

[tex]7\frac{3}{8}[/tex] pounds

Step-by-step explanation:

First, convert the fractions into improper fractions, and make them have the same denominator.

First package: [tex]3\frac{3}{4} =\frac{15}{4}=\frac{30}{8}[/tex]

Second package: [tex]1\frac{1}{8} =\frac{9}{8}[/tex]

Third package: [tex]2\frac{1}{2}=\frac{5}{2}=\frac{20}{8}[/tex]

Notice that all the fractions have the same denominator, making it easy to add up. Now we add up the fractions.

[tex]\frac{30}{8}+\frac{9}{8}+\frac{20}{8}=\frac{59}{8} =7\frac{3}{8}[/tex]

Ethan has a piece of string that is 6 meters long. He cuts the string into 3 pieces of equal length. How many centimeters long is each piece of string?

Answers

9514 1404 393

Answer:

  200 cm

Step-by-step explanation:

1 meter is 100 cm, so 6 meters is 600 cm. Each piece is 1/3 of that, so is ...

  (600 cm)/3 = 200 cm . . . length of each piece

Find the measure of the line segment indicated, assume that lines which appear tangent are tangent. (2 questions) PLS help with these problems ! Pls don't just do it for points

Answers

Answer:

1

Step-by-step explanation:

The probability of being a universal donor is 6% (O-negative-blood type). Suppose that 6 people come to a blood drive.
a) What are the mean and standard deviation of the number of universal donors among the 6 people?
b) What is the probability that there are exactly three universal donors?

Answers

Using the binomial distribution, it is found that:

a) The mean is of 0.36 and the standard deviation is of 0.58.

b) There is a 0.0036 = 0.36% probability that there are exactly three universal donors.

What is the binomial distribution formula?

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

The values of the parameters are given as follows:

n = 6, p = 0.06.

Item a:

E(X) = np = 6 x 0.06 = 0.36.[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{6 \times 0.06 \times 0.94} = 0.58[/tex]

The mean is of 0.36 and the standard deviation is of 0.58.

Item b:

The probability is P(X = 3), hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 3) = C_{6,3}.(0.06)^{3}.(0.94)^{3} = 0.0036[/tex]

There is a 0.0036 = 0.36% probability that there are exactly three universal donors.

More can be learned about the binomial distribution at https://brainly.com/question/24863377

#SPJ1

If f(x)=(x-3)^2+1 what is f(6)

Pls help

Answers

Answer:

I love algebra anyways  

the ans is in the picture with the steps  

(hope it helps can i plz have brainlist :D hehe)

Step-by-step explanation:

If function g has the factors (x - 7) and (x + 6), what are the zeros of function g?
ОА.
-7 and 6
OB.
-6 and 7
Oc.
6 and 7
OD
-7 and -6

Answers

Answer:

7 and -6

Step-by-step explanation:

Given

Factors: (x - 7) and (x + 6)

Required

Determine the zeros

To do this, we simply equate the factors to 0

[tex]x - 7 = 0[/tex]

[tex]x = 7[/tex]

[tex]x + 6 = 0[/tex]

[tex]x = -6[/tex]

So, the zeros are -7 and 6

What is 26% of 50?
plz help

Answers

Answer:

13

Step-by-step explanation:

50 multiplied by .26

I tried finding this one earlier and it didn’t work , so please help again !

Answers

Answer:

C. 62

Step-by-step explanation:

All angles in a triangle are equivalent to 180. First find angle C. Which is 64. then subtract that by 180, which is 116. after that we combine like terms then solve for X. Combine like terms: 5x-9=116 X=25 We plug X into angle's A equation. And you get 62. hope this helps :)

Find the bearing of the ship. Round to the nearest tenth of a degree if necessary.

Answers

9514 1404 393

Answer:

  117°

Step-by-step explanation:

We assume you want to report your bearing as an angle measured CW from North. For conventional angles greater than 90°, it will be ...

  450° -angle = 450° -333° = 117°

The bearing of the ship is 117°.

someone please help me answer this

Answers

84 is the answer I think

Answer:

a = 72 mm is the answer.

Step-by-step explanation:

a = ?

b = 21 mm

c = 75 mm

According to the Pythagoras theorem

a² + b² = c²

a² + 21² = 75²

a² + 441 = 5625

a² = 5625 - 441

a² = 5184

a = 72 mm

∴ a = 72 mm is the length of the missing leg.

Please help me answer this. I’ll give a reward. To who every answers it correctly.

Answers

Answer:

66

Step-by-step explanation:

55+59 =114

180-114=66


please help answer

Answers

After all that typing in the comments, LOL. The hardest part was figuring out the area of the stripes. I put those calculations off to the right. Please let me know if you can’t read my writing.

4(3√x-2)+1=9. what is the solution to this equation

Answers

x=16/9
hope this helped

Answer:

x=22/9

Step-by-step explanation:

4(3√(x-2))+1=9

4(3√(x-2))=8

3√(x-2)=2

√(x-2)=2/3

x-2=4/9

x=4/9+2

x=4/9+18/9

x=22/9

Therefore, the solution is x=22/9

Please answer number number 7 I’ll give brainliest thank you!

Answers

Answer:

b) $41.85

Step-by-step explanation:

Discount = Original Price x Discount %/100

Discount = 45 × 7/100

Discount = 45 x 0.07

You save = $3.15

Final Price = Original Price - Discount

Final Price = 45 - 3.15

Final Price = $41.85

hope this helps and is right. p.s. i really need brainliest :)

Answer:

Step-by-step explanation:

that would be A

A dragonfly can travel 72 miles in 2 hours at a constant rate. How fast can it fly?
A. 18 mph
B. 36 mph
C. 48 mph
D. 73 mph

Answers

the answer is B because you divid 72 by 2

I need help...WILL GIVE BRAINLIEST !!!!!

Answers

Answer:

Step-by-step explanation:

48 is preimeter

96 is the area

Make me brainliest

Can someone please find the slope, no link answers pls

Answers

Answer:

-3/1

Step-by-step explanation:

The rise is 1 and the the run is 3 but the line goes from top left to top right so its negative.

Can anybody help me on this question?

Answers

Answer:

60

Step-by-step explanation:

i did the math yeah

The answer is 60 . ........

PLEASE HELP !! ILL GIVE BRAINLIEST !!

Answers

Answer:

<QPM and <QPR

Step-by-step explanation:

adjacent angles have a common vertex and side, and those are the only two that have a common side

hope this helps :)

if it does, can I get brainliest, please??!

Esteban wants to take out a $5,000 loan from the bank and is offered two choices. If he pays the loan back within 3 years, he will make monthly payments of $148.07. If he pays the loan back within 5 years, he will make monthly payments of $92.53. How much more will he pay in interest ifhe chooses the 5-year loan???

Answers

Answer:

ESTEBAN IS FOKING BROKE

Step-by-step explanation:

What is the most likely meaning of the word endangered?

influenced

exposed

assisted

threatened

Answers

Answer:

exposed is another word for endangered

Exposed is another word for endangered
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