Exercise 5.16.1: 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. Solution (b) There are at least two consecutive flips that come up heads.

Answers

Answer 1

Answer:

[tex](a)\ Pr = 0.25[/tex]

[tex](b)\ Pr = 0.50[/tex]

Step-by-step explanation:

Given

[tex]Flips = 4[/tex]

First, we calculate the sample size;

The coin has two possible outcomes (i.e. head or tail) and the number of flips is 4.

So, the sample size (N) is:

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

[tex]N = 16[/tex]

Solving (a): Probability the outcome of the first and last flip is head.

The possible outcomes for this event are:

[tex]n = \{(HHHH), (HHTH), (HTHH),(HTTH)\}[/tex]

[tex]n(n) = 4[/tex]

The probability is:

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

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

[tex]Pr = 0.25[/tex]

 

Solving (a): Probability that the outcome of at least 2 consecutive flips is head.

The possible outcomes for this event are:

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

[tex]n(n) = 8[/tex]

The probability is:

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

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

[tex]Pr = 0.50[/tex]


Related Questions

The sum of the lengths of two opposite sides of the circumscribed quadrilateral is 12 cm, the length of a radius of the circle is 5 cm. Find the area of the quadrilateral

Answers

Answer:

60cm^2

Step-by-step explanation:

We assume that is a circumscribing quadrilateral, rather than one that is circumscribed. It is also called a "tangential quadrilateral" and its area is ...

 K = sr

where s is the semi-perimeter, the sum of opposite sides, and r is the radius of the incircle.

 K = (12 cm) (5cm) = 60 cm²

_____

A quadrilateral can only be tangential if pairs of opposite sides add to the same length. Hence the given sum is the semiperimeter.

1/3 of 36 solve using a tape diagram

Answers

That would be 12! I’m not sure what a tape diagram is but the answer is that. 1/3 * 36= 12

What is the median for this list of numbers? 3, 6, 9, 10, 12

Answers

the answer is 9 because if you put those numbers in a life from smallest to biggest and take one off each side your left with 9

Answer:

9

Step-by-step explanation:

what is the probability if you randomly select comedy book replace it and another comedy book?
(if your going to answer pls explain )

Answers

Oh pls help me

Jake tossed a paper cup 50 times and recorded how it landed. The table shows the results:

Position Open Side Up Closed Side Up Landing on Side
Number of Times Landed in Position 3 7 40


Based on the table, determine the experimental probability of each outcome (landing open side up, landing closed side up, and landing on its side). Show your work. (10 points)

Find GH. What does GH equal?

Answers

Answer: GH = HJ = 4.6

Step-by-step explanation:

Answer: GH = HJ = 4.6

A statement is shown. ​"The square root of x is a number that is non-terminating and non-repeating." ​Select all of the values of x that make the statement true.
a: x=1
b: x=8
c:x=25
d: x=81
e: x=125

Answers

Answer:

its B and E

Step-by-step explanation:

If you put two straight angles together, you get an angle that is 360°. You can think of this
angle as turning all the way around so that you are facing the same direction as when you
started the turn.
380

Answers

Answer:

what is your question?

Step-by-step explanation:

Could someone explain to me how to solve any one of these problems so that I could solve the rest of them on my own? I already know the asymptote and the y-intercept, but I'm unsure of how to find the maximum/minimum.

Answers

Answer:

what in the world is this

Answer: Maybe asymptote means the lowest number and y-intercept means the second lowest and minimum means medium and maximum means the highest  number.

I'm sorry if this doesn't help but i'm still in 3rd grade.

How do you refer 2ml of blue and 6ml of green in batches

Answers

Answer:

8ml

Step-by-step explanation:

Help please what is this?

Answers

Ask your mom .............................

what equation describes a line that has a slope of 4/5 and a y-intercept of 2/5

Answers

Answer:

y = 4/5 x + 2/5

Step-by-step explanation:

What is the surface area of this rectangular prism i-ready

Answers

Answer:

290 in²

Step-by-step explanation:

Using the net of the box given, we can see that there are 4 equal rectangles and 2 equal squares that make up the prism.

Area of the 4 rectangles = 4(60) = 240 in²

Area of the 2 squares = 2(25) = 50 in²

Therefore,

Surface Area of the prism = 240 + 50 = 290 in²

Answer:

The surface area of this prism is 290(in)²

Step-by-step explanation:

The surface area of a box is equal to the sum of the areas of each side of the box.

[tex]2 \times (lenght) \times (widht) + 2 \times (lenght) \times (height) + 2 \times (widht) \times (height)[/tex]

Substitute the values of the length l=5, the width w=5, and the height h=12 into the formula.

[tex]2 \times 5 \times 5 + 2 \times 5 \times 12 + 2 \times 5 \times 12[/tex]

Simplify each term.

[tex]50 + 120 + 120[/tex]

Simplify by adding numbers.

[tex]290(in)^{2} [/tex]

Hence, The surface area of this rectangular prism is 290in².

Imagine the average time to complete a 4-year bachelor degree is actually 4.7 years, based on national data. You collect data on the 68 psychology students who started school during the same semester as you, finding an average time to complete at 4.3 years with a standard deviation of 0.6 years. What would be the effect size associated with a single-sample t test

Answers

Answer:

-0.67

Step-by-step explanation:

Given that :

Population mean, μ = 4.7

Sample size, n = 68

Sample mean, M = 4.3

Sample standard deviation, s = 0.6

The effect size, d can be obtained using the relation :

d = (M - μ) / s

d = (4.3 - 4.7) / 0.6

d = - 0.4 / 0.6

d = - 0.66666

d = - 0.67

Hence, effect size associated with a single-sample t test is - 0.67

Sandi's
house
School
2.5 in.
Sandi lives 5 miles from her school. One day, she took
the bus from her house to school. After school, she
went to the library to pick out a book. Then she went to
the park to read. If Sandi traveled along the route
shown, how far did she travel in all?
3 in.
miles
1.5 in.
Library
Park!

Answers

Answer: the answer is 14

what is the value of x in each figure

PLEASE DON'T GIVE ME A LINK ​

Answers

Answer:

x=43

Step-by-step explanation:

3x+17+x-9=180

4x+8=180

4x=180-8

4x=172

x=43

X= 43 is the answer

Here is my question please help.

Answers

It would be 22 since they are congruent
The answer would be 22 hope that helps

3) Determine the greatest common factor between
Xy2 and x6y2

Answers

Answer:

it would be GCF= xy^2

Step-by-step explanation:

because you have to put the lowest variable for the GCF, therefore, its only 1 x and then y^2

solve for x:
(1/x) + (1/2x) = 18

Answers

Answer:

/sorry/

Step-by-step explanation:

How to solve your problem

(1)+(12⋅)=18

\frac{x}{(\frac{1}{x})}+(\frac{1}{2} \cdot x)=18

(x1​)x​+(21​⋅x)=18

Solve

1

Combine multiplied terms into a single fraction

(1)+(12)=18

\frac{x}{(\frac{1}{x})}+(\frac{1}{2}x)=18

(x1​)x​+(21​x)=18

(1)+(12)=18

\frac{x}{(\frac{1}{x})}+(\frac{1x}{2})=18

(x1​)x​+(21x​)=18

2

Multiply by 1

3

Eliminate redundant parentheses

Solution

(1)+2=18

one of your friends is heading north for a holiday and the oter friend is heading south. if their destinies are 1029 miles apart and one car is traveling at 45 miles per hour and the other at 58 mile sper hour how many hours before the 2 cars pass eacother

Answers

Answer: 1029 + 45 + 58 + 2 = 1134

Step-by-step explanation: If you read the problem it has a key word how many so all you have to do is add.

In the image below the area of the shaded sector is

Answers

Answer:

area = 471 ft²

Step-by-step explanation:

area of full circle = π30² = 2826 ft²

(60°/360°)(2826) = 471 ft²

A group of friends went to play minigolf at Adventureland. Anna's score was 26 putts, Daniela's score was 31 putts, Luiza's score was 39 putts, and Vera's score was 32 putts.
Find the mean absolute deviation (MAD) of the data se

Answers

Answer:

3.5

Step-by-step explanation:

Please help I need this due in 3 minutes!

Answers

Answer: you just add 700 and 750 which will give us 1,450

Step-by-step explanation:

The factors of 30 are 1 2 3 4 5 6 10 15 and 30 Which if these are prime factors??​

Answers

Answer: 1,2,3,5,

Step-by-step explanation: 1,2,3,5 are prime numbers because they are not a product of two smaller numbers.

The Pythagorean Theorem can be used to find missing side lengths of any type of triangle.

Answers

Answer:

False, it can only be used for Right Triangles.

Step-by-step explanation:

Answer:

false

Step-by-step explanation:

Terry used a bag of marbles to do a probability experiment. In the experiment, he selected one marble at random from the bag, recorded the color, and put the marble back in the bag. He repeated this procedure 15 times and recorded the results in the table shown Based on the results, what is the probability that the next marble Terry selects will be a green marble? Mark all that apply.

Answers

Answer:

Mate there isn't a chart

Step-by-step explanation:

TIMED PLS HELP ME IM BEGGING

Answers

Answer:

4 cm

Step-by-step explanation:

Cylinder Volume formula:

V = πr²h

Given:

V = 240π

h = 15

Finding r:

V = πr²h

240π = πr²(15)

r² = 240π/15π

r² = 16

[tex]\sqrt{r^2} =\sqrt{16}[/tex]

r = 4

Answer:

4 cm

Step-by-step explanation:

TTr^2h = 240TTcm^3(the TT cancel out)r^2 x 15 = 240cm^3(divide both sides by 15)r^2 = 16(square root both sides)r = 4cm

help! help! please help ​

Answers

Answer:

to answer this i am gonna need the rise and run or the y2 -x2/ y1-x1 and then i well come back and edit this to the right answer

Step-by-step explanation:

Zane is putting the strings on 5 harps. Each harp has 48 strings.
How many strings does Zane need for all 5 harps?

Answers

Answer:

Zane needs 240 strings for 5 harps.

Step-by-step explanation:

All you have to do is multiply

48 * 5 = 240

So, the answer is 240

Hope this helps! :)

Which statement about the data is true and find the median and range.

Answers

Answer:

I think it's D

its either A or D because the median is definitely 4

A dice is rolled 50 times.
The score of each throw is recorded in the table below.
Score
1
2
3
4
5
6
Frequency
12
9
5
13
3
8
12
a) The relative frequency of scoring a 1 was calculated as = 0.24
50
Work out the relative frequency, as a decimal, of throwing a 2.
I
[1]
b) How many times would you expect to roll a 5 when
this dice is thrown 3000 times?
[2]
c) How many times would you expect to roll a 5 when
a fair dice is thrown 3000 times?
+
[2]

Answers

The answer is 123456789 oh I mean I dont know
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