# 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)...

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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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`