427 Twenty percent of the population of a particular city we

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Twenty percent of the population of a particular city wear glasses. If you randomly stop people from that city, determine the following probabilities: It takes exactly 10 tries to get the third person who wears glasses. It takes at least 10 tries to get the third person who wears glasses.

Solution

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

a)
Out of 9 selected 2 wear glasses
P( X = 2 ) = ( 9 2 ) * ( 0.2^2) * ( 1 - 0.2 )^7
= 0.302
Probability of 10th wear glass = 0.302*0.20 = 0.0604

  
b)
P( atleast 10 person selected to find 3 wear glasses) = 1 - P(We only have 2 selected glasses from 10 selected)

P(We only have 2 selected glasses from 10 selected) = P( X = 2 ) = ( 10 2 ) * ( 0.2^2) * ( 1 - 0.2 )^8
= 0.302

P( atleast 10 person selected to find 3 wear glasses) = 1 - 0.302 = 0.698