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Last winter in a certain area 2/5 of the population caught the flu. Four people from...

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user97 | Student, Undergraduate | (Level 1) eNoter

Posted April 15, 2013 at 4:19 PM via web

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Last winter in a certain area 2/5 of the population caught the flu. Four people from this area are selected at random. Calculate the probability that

(i) all four caught the flu last winter

(ii) all four survived the winter without catching the flu

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mariloucortez | High School Teacher | (Level 3) Adjunct Educator

Posted April 16, 2013 at 5:50 AM (Answer #1)

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You can use Binomial Distribution to solve this problem.

Binomial Distribution is given by:

`nC_x * p^x * q^(n-x)`

where n is the total number of samples

          x is 0,1,2 and so on

          p is the success rate (in this case, it is the percentage of population      getting flu)

          q is 1-p or the failure rate (in this case, it is the percentage of population not getting flu)

So before using the formula, identify first the given.

n = 4

p = 2/5

q = 1-2/5 = 3/5

(i) For the probability if all 4 get flu.

`(i) P(x=4) = 4C_4 * (2/5)^4 * (3/5)^0`

`(i)P(x=4) = 16/625 = 0.0256`

(ii) For the probability if all 4 survuived the flu.

`(ii) P(x=0) = 4C_0 * (2/5)^0 * (3/5)^4`

`(ii) P(x=0) = 0.1296`    

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