423 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 a person who wears glasses. It takes at least 10 tries to get a 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