SOLUTION: 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

Algebra ->  Statistics  -> Binomial-probability -> SOLUTION: 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      Log On


   

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?

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
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. 


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


      P = C%5B7%5D%5E4%2A0.7%5E4%2A%281-0.7%29%5E%287-4%29 = %28%287%2A6%2A5%29%2F%281%2A2%2A3%29%29%2A0.7%5E4%2A0.3%5E3 = 0.2269  (rounded).    ANSWER



(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).    ANSWER



(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).    ANSWER

Solved.

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If you want to see many similar or different solved problems on binomial distribution probability,  look into the lessons
    - Simple and simplest probability problems on Binomial distribution
    - Typical binomial distribution probability problems
    - How to calculate Binomial probabilities with Technology (using MS Excel)
    - Solving problems on Binomial distribution with Technology (using MS Excel)
    - Solving problems on Binomial distribution with Technology (using online solver)
in this site.

After reading these lessons,  you will be able to solve such problems on your own,
which is your  PRIMARY  MAJOR  GOAL  visiting this forum  (I believe).