Question

A town has 30% foreigners living all over the town and all the inhabitants of the town use
public transport. What is the probability that at least 5 of the 15 people waiting in the
queue for the metro are local people?

Answer 1

Given :  A town has 30% foreigners living all over the town and all the inhabitants of the town use public transport.

To find : probability that at least 5 of the 15 people waiting in the queue for the metro are local people​

Solution:

A town has 30% foreigners living all over the town

Hence locals living in town = 100 - 30 = 70 %

probability of local person p = 0.7

Probability of foreigner q = 1 -p = 0.3

n = 15

P(x) = ⁿCₓpˣqⁿ⁻ˣ

probability that at least 5  people waiting in the queue for the metro are local people​

= 1 - P(0) - P(1) - P(2) - P(3) - P(4)  

P(0) =  ¹⁵C₀(0.7)⁰(0.3)¹⁵  

P(1) =  ¹⁵C₁(0.7)¹(0.3)¹⁴

P(2) =  ¹⁵C₂(0.7)²(0.3)¹³

P(3) =  ¹⁵C₃(0.7)³(0.3)¹²

P(4) =  ¹⁵C₄(0.7)⁴(0.3)¹¹

= 1 - 0.000672

= 0.999328  

= 99.9328 %

probability that at least 5 of the 15 people waiting in the queue for the metro are local people​ =  0.999328    or 99.9328 %  

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