In a large population, 60% of the people have been vaccinated. If 4 people are randomly selected, what is the probability that AT LEAST ONE of them has been vaccinated?

Give your answer as a decimal to 4 places.

Answers

Answer 1

Answer:

0.9744 probability that AT LEAST ONE of them has been vaccinated

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they have been vaccinated, or they have not. The probability of a person having been vaccinated is independent of any other person. So 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.

60% of the people have been vaccinated.

This means that [tex]p = 0.6[/tex]

If 4 people are randomly selected, what is the probability that AT LEAST ONE of them has been vaccinated?

This is

[tex]P(X \geq 1)[/tex] when [tex]n = 4[/tex].

We have that

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

In which

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

[tex]P(X = 0) = C_{4,0}.(0.6)^{0}.(0.4)^{4} = 0.0256[/tex]

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0256 = 0.9744[/tex]

0.9744 probability that AT LEAST ONE of them has been vaccinated


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Answers

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Answers

Answer:

6

Step-by-step explanation:

cause 3+3 is 6

thanks for the easy points :3

Answer:

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Answers

841 rounded to the nearest 10th is 840...hope this helps u :)

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Answer:

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Step-by-step explanation:

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Answer:

i think the answer is

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Answers

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Answers

Answer:

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Step-by-step explanation:

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Answers

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Answers

There are 2 answers to this question

First Answer:

1+1=2

Second Answer:

Window

Explanation:

1 goes on the top

1 goes on the bottom

The first - of the = goes on the side

The second - of the = goes on the other side

The + sign goes in the middle

Heres a picture example:

I hope this helps you have a good day/night/afternoon

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Answers

Answer:

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Step-by-step explanation:

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Answer:

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Answer:

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Step-by-step explanation:

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Answer:

12

Step-by-step explanation:

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A student wrote and simplified an expression to find the perimeter of this 5 points
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Answer:

Step 4.          

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Answers

Answer:

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Answer:

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48 acopf70 (eg)3 (nt)2

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Answers

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Step-by-step explanatio x 4=

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Answers

Answer:

The more familiar unit of measurement is that of degrees. A circle is divided into 360 equal degrees, so that a right angle is 90°.

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Answers

Step-by-step explanation:

Here's another solution.

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ratio 3:10

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Answers

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-
-
-
Explanation:

I think you meant [tex]2^{4}[/tex] and [tex]3^{2}[/tex]. With exponents, you don't add the number and the exponent. What you have to do is the first number times itself, and let's use number one as an example. So, since it's four you have to do this.
-
-
[tex]2^4[/tex]= 2 x 2 x 2 x 2= 16

and for problem number two, it's the same thing but different numbers.

[tex]3^{2}[/tex]= 3 x 3 x 3= 9
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-
now, all you have to do is add [tex]16+9= 25[/tex]

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Answers

Answer:

Step-by-step explanation:

Graph given in the attachment represents a linear function f(x).

y = -f(x) represents the reflection of the graph across x-axis.

Therefore, y-coordinates of the points on the graph will get opposite notation after the reflection across x-axis.

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Answers

Answer:

x^2+3x−10

Step-by-step explanation:

X^2+3x-10

First multiply x with (x-2)Next multiply 5 with (x-2) with + sign between them

x(x-2)+5(x-2)

X^2–2x+5x-10

X^2+3x-10

Answer: x^2-2x+5x-10

Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Answer:b

Step-by-step explanation: took the test

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Answers

Answer:

Step-I’m going to need more information

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