Richard has just been given an l0-question multiple-choice quiz in his history class. Each question has five answers, of which only one is correct, Since Richard has not attended a class recently, he doesn't know any of the answers, Assuming that Richard guesses on all 10 questions. Find the indicated probabilities.
A) What is the probability that he will answer all questions correctly?
B) What is the probability that he will answer all questions incorrectly?
C) What is the probability that he will answer at least one of the questions correctly?
Then use the fact that P(r1) = 1 P(r = 0).
D) What is the probability that Richard will answer at least half the questions correctly?

Answers

Answer 1

Answer:

a) 0.0000001024 probability that he will answer all questions correctly.

b) 0.1074 = 10.74% probability that he will answer all questions incorrectly

c) 0.8926 = 89.26% probability that he will answer at least one of the questions correctly.

d) 0.0328 = 3.28% probability that Richard will answer at least half the questions correctly

Step-by-step explanation:

For each question, there are only two possible outcomes. Either he answers it correctly, or he does not. The probability of answering a question correctly is independent of any other question. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

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

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

Each question has five answers, of which only one is correct

This means that the probability of correctly answering a question guessing is [tex]p = \frac{1}{5} = 0.2[/tex]

10 questions.

This means that [tex]n = 10[/tex]

A) What is the probability that he will answer all questions correctly?

This is [tex]P(X = 10)[/tex]

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

[tex]P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} = 0.0000001024[/tex]

0.0000001024 probability that he will answer all questions correctly.

B) What is the probability that he will answer all questions incorrectly?

None correctly, so [tex]P(X = 0)[/tex]

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

[tex]P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074[/tex]

0.1074 = 10.74% probability that he will answer all questions incorrectly

C) What is the probability that he will answer at least one of the questions correctly?

This is

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

Since [tex]P(X = 0) = 0.1074[/tex], from item b.

[tex]P(X \geq 1) = 1 - 0.1074 = 0.8926[/tex]

0.8926 = 89.26% probability that he will answer at least one of the questions correctly.

D) What is the probability that Richard will answer at least half the questions correctly?

This is

[tex]P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)[/tex]

In which

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

[tex]P(X = 5) = C_{10,5}.(0.2)^{5}.(0.8)^{5} = 0.0264[/tex]

[tex]P(X = 6) = C_{10,6}.(0.2)^{6}.(0.8)^{4} = 0.0055[/tex]

[tex]P(X = 7) = C_{10,7}.(0.2)^{7}.(0.8)^{3} = 0.0008[/tex]

[tex]P(X = 8) = C_{10,8}.(0.2)^{8}.(0.8)^{2} = 0.0001[/tex]

[tex]P(X = 9) = C_{10,9}.(0.2)^{9}.(0.8)^{1} \approx 0[/tex]

[tex]P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} \approx 0[/tex]

So

[tex]P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0264 + 0.0055 + 0.0008 + 0.0001 + 0 + 0 = 0.0328[/tex]

0.0328 = 3.28% probability that Richard will answer at least half the questions correctly


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Step-by-step explanation:

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Lexi mailed a letter on Monday morning. The letter traveled 1/2 of a mile on Monday. It
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Answers

Answer:

1 1/4 miles

Step-by-step explanation:

3/4 + 2/4 (1/2 = 2/4) = 5/4 = 1 1/4

Which answers describe the shape below? Check all that apply.
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Answer:

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Step-by-step explanation:

A school buys 1,950 pencils. The pencils are sold in boxes, with 30 pencils in each box. If each box costs $4.05, what is the total cost, in dollars, that the school will pay for the pencils?

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The answer is
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work out the circumference of this circle

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14cm​

Answers

Answer:

43.96

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

Circumference of the circle

= 2πr

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How was Franklin D. Roosevelt a lasting impact even on today's society​

Answers

Answer:

Franklin Delano Roosevelt, often referred to by his initials FDR, was an American politician who served as the 32nd president of the United States from 1933 until his death in 1945. A member of the Democratic Party, he won a record four presidential elections and became a central figure in world events during the first half of the 20th century. Roosevelt directed the federal government during most of the Great Depression, implementing his New Deal domestic agenda in response to the worst economic crisis in U.S. history. As a dominant leader of his party, he built the New Deal Coalition, which defined modern liberalism in the United States throughout the middle third of the 20th century. His third and fourth terms were dominated by World War II, which ended shortly after he died in office.

Step-by-step explanation:

to this ‘Great Man Theory’ it can be said that Franklin Delano Roosevelt upheld his victorious and highly regarded government through means of social, economic and political reforms, as well as ambitious personal and strategic decisions that have successfully remained influential to American society today and maintained his image as a prominent historic leader.

Please can yo help me I am very bad at word problems.

Answers

Answer:

1. 60, 122 feet

2. a + s = 12

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Step-by-step explanation:

I can't do all of them but I'll do the first 2:

1.

let w be the width of the rectangle

Then the length would be 2w + 2

Using those, the perimeter would be:

2w + 2 + 2w +2 + w + w = 364

solving:

[tex]6w + 4 = 364\\6w = 360\\w = 60[/tex]

This means the length would be:

[tex]2(60)+2\\120 + 2\\122[/tex]

2.

let a be the number of adult tickets

let s be the number of student tickets

Then:

The total number of tickets is 12, so:

a + s = 12

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Answers

Answer:

Step-by-step explanation:

a)

2.64÷3.3  ( said  2.64 divided by 3.3)

3.3√2.64  ( yes I know it's not the division sign but it's as close as we can get)

2.64 / 3.3

All three representations  are the same. each say  divide 2.64 by 3.3. If you're thinking that last one looks more like a fraction, you're right, but.. that's also what that means.   I'm showing these different ways to express the idea of division b/c it's part of what is involved with showing the work and understanding it.

so, to do the above let's move the decimal point to the right .. and do we want to move it one or two places.  :?  one because of 3.3 or two , because of 2.64, well we want to move it so we don't have to think about it in the problem... so move it the biggest amount that you need to, get the the decimil out of both numbers.. since the 2.64 needs two moves to the right of the decimal... use 100 times  to move it 2 places, If you needed 3 then use 1000, 4 , 10,000 ect ect... see the pattern?

so

100(3.3 √ 2.64 )

move the decimal point in both 2 places right

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I put the extra zeros in, just so you can see the decimal easy.  The zeros to the right of the decimal make no difference here.

now I'll know to put the number that I use to divde with above the zero,  of 264.0  .. and i'll think about how many times 3 goes into 26 ,without going over.  3*8 = 24 so I want an 8

    ↓ ←   ←  ← 0.8

330.0 √ 264.0      ( multiply  8 * 330 = 2640 )

    ↓ →   -264 .0      ( subtract 2640 from the number above )

                       0

you are done with that one, since there is zero left over and   0.8 is the answer

b)

0.324 ÷ 0.27

0.27 √ 0.324

0324 / 0.27

1000( 0.27 √ 0.324)

270 √ 324.0

  ↓  ←  ←  1.2

270 √ 324.0

 ↓→   - 270   ( multiply by the 1 )

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 ↓→       - 540  (multiply by the 2 )

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since there is zero left over you are done. The answer is  1.2

C)

0.32 ÷ 0.16

0.16 √ 0.32

100(0.32 / 0.16)

↓ ←   2

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zero left over you are done.  the answer is 2 :)

d)

16.92 ÷ 9.4

9.4 √ 16.92

100(16.92 / 9.4)

  ↓   ←  ←  1.8

940 √1692.0

 ↓→→ - 940       (multiply by 1 )

 ↓        7520

 ↓→  -  7520      (multiply by 8 )

                 0

since there is zero left you are done,  The answer is  1.8

that was a lot, really nobody has talked or told you how to do this before?  

where is your teacher?  :/  

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[tex]r \geqslant 5.5[/tex]

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Answers

Hyp²=ADJ²+OPP²

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Answers

Answer:

a) 1.6 x 10 ^6 dollars.

Step-by-step explanation:

since President Ronald Reagan served for 8 years. So the total amount of money that he earned is 2 x 10^5 x 8 = 16 x 10 ^ 5 = 1.6 x 10^6 dollars.

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Answers

Answer:

x = 35°

Step-by-step explanation:

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Answers

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253 boxes

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Answers

Answer:

12

Step-by-step explanation:

First,

Add 45+52+15

Then the answer will be 112

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Answer:

18 students

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30 + 37 + 15 = 82

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Answers

Answer: Hello the statement related to your question is missing attached below is the statement

answer : The statement is false

Step-by-step explanation:

The statement is false

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Answers

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Answer:

B

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

because they are telling you that the 7th graders were randomly chosen out of everyone who rides in a car to school to be fractioned out.

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Answers

Answer:

Joe Mok

Step-by-step explanation:

Joe MAMA

Consider the parabola given by the equation: f(x) = 2x2 + 14.0 – 4
Find the following for this parabola:
A) The vertex:
B) The vertical intercept is the point
C) Find the coordinates of the two z intercepts of the parabola and write them as a list, separated by
commas:
It is OK to round your value(s) to to two decimal places.

Answers

Answer:

Step-by-step explanation:

f(x)  = 2x² + 14x - 4

= 2(x² + 7x) - 4

= 2(x² +7x + 3.5²) - 2(3.5²) - 4

= 2(x+3.5)² - 28.5

vertex (3.5, -28.5) = (7/2, -57/2)

The vertical intercept is the y-intercept, i.e., f(0) = -4.

The x-intercepts are the values of x for which y=0.

2x² + 14x - 4  = 0

x = [-14±√(14²-4(2)(-4))]/[2(2)] = [-7±√57]/2 ≅ -7.27, 0.27

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