Question 1193100
.
A survey shows that about 70 % of those over the age of 65 years old 
are in danger of catching COVID-19. 
If 7 persons over the age of 65 are randomly selected, answer the following questions:
a) What is the probability exactly 4 of the 7 have COVID-19?
b) What is the probability at most 1 of the 7 has COVID-19?
c) What is the probability at least 2 of the 7 have COVID-19?
~~~~~~~~~~~~~



            These are standard problems on binomial distribution.



<pre>
(a) - number of trials         n =  7;
    - number of success trials k =  4;
    - Probability of success on a single trial p = 0.7.


      P = {{{C[7]^4*0.7^4*(1-0.7)^(7-4)}}} = {{{((7*6*5)/(1*2*3))*0.7^4*0.3^3}}} = 0.2269  (rounded).    <U>ANSWER</U>



(b) - number of trials         n =  7;
    - number of success trials k <= 1;   (k = 0, 1)
    - Probability of success on a single trial p = 0.7.


      Use online free of charge calculator https://stattrek.com/online-calculator/binomial.aspx

          P = P(n=7; k<=1; p=0.7) = 0.003791  (rounded).    <U>ANSWER</U>



(c) - number of trials         n =  7;
    - number of success trials k >= 2;   (k = 2,3,4,5,6,7)
    - Probability of success on a single trial p = 0.7.


      You may use online free of charge calculator https://stattrek.com/online-calculator/binomial.aspx

          P = P(n=7; k>=2; p=0.7) = 0.9962  (rounded), 

      or simply notice that this probability is the complement to that found in part (b)

          P = 1 - 0.003791 = 0.9962  (the same value).    <U>ANSWER</U>
</pre>

Solved.


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If you want to see many similar or different solved problems on binomial distribution probability, &nbsp;look into the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Solving-problems-on-Binomial-distribution-manually.lesson>Simple and simplest probability problems on Binomial distribution</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Typical-binomial-distribution-probability-problems.lesson>Typical binomial distribution probability problems</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/How-to-calculate-binomial-probabilities-using-Technology.lesson>How to calculate Binomial probabilities with Technology (using MS Excel)</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Solving-problems-on-Binomial-distribution-using-Technology.lesson>Solving problems on Binomial distribution with Technology (using MS Excel)</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Solving-problems-on-Binom-distr-with-Technology-%28using-online-solver%29.lesson>Solving problems on Binomial distribution with Technology (using online solver)</A> 

in this site.


After reading these lessons, &nbsp;you will be able to solve such problems on your own, 

which is your &nbsp;PRIMARY &nbsp;MAJOR &nbsp;GOAL &nbsp;visiting this forum &nbsp;(I believe).