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

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

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Answer:

8ml

Step-by-step explanation:

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:

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
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[2]
c) How many times would you expect to roll a 5 when
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+
[2]

Answers

The answer is 123456789 oh I mean I dont know

solve for x:
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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

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Answers

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

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:

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

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:

Here is my question please help.

Answers

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

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.

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:

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.

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 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.

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Answers

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

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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:

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Answers

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Answers

Answer: GH = HJ = 4.6

Step-by-step explanation:

Answer: GH = HJ = 4.6

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Answers

Oh pls help me

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Find the mean absolute deviation (MAD) of the data se

Answers

Answer:

3.5

Step-by-step explanation:

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a: x=1
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e: x=125

Answers

Answer:

its B and E

Step-by-step explanation:

Sandi's
house
School
2.5 in.
Sandi lives 5 miles from her school. One day, she took
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went to the library to pick out a book. Then she went to
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miles
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Answers

Answer: the answer is 14

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Answers

Answer:

I think it's D

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Answers

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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

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Answers

Answer:

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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:

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Step-by-step explanation:

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Answers

Answer:

x=43

Step-by-step explanation:

3x+17+x-9=180

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4x=180-8

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Answers

Answer:

it would be GCF= xy^2

Step-by-step explanation:

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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

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