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.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

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

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

60% of the people have been vaccinated.

This means that $p = 0.6$

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

This is

$P(X \geq 1)$ when $n = 4$ .

We have that

$P(X \geq 1) = 1 - P(X = 0)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{4,0}.(0.6)^{0}.(0.4)^{4} = 0.0256$

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0256 = 0.9744$

0.9744 probability that AT LEAST ONE of them has been vaccinated

5 0

3 years ago

1/3 divided by 2/5 help me plss

stepladder [879]

Answer:

5/6

Step-by-step explanation:

dividing means you gotta flip it to multiplication.

1 times 5 = 5

3 times 2 = 6

6 0

3 years ago

Micheal has saved 27 quarters from washing cars. How many cents does Michael have?

igomit [66]

Micheal has saved 27 quarters from washing cars. Micheal has 675 cents

7 0

4 years ago

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Explain how proving two triangles congruent can help prove parts of the triangle congruent.

Ierofanga [76]

You can use the CPCTC (Corresponding Parts of Congruent Triangles are Congruent) property. This means that when two triangles are congruent, all the corresponding parts are congruent to each other.

Have an awesome day! :)

8 0

3 years ago

Read 2 more answers