Qi.(10\') In a group of households, 60% of the households live in New Temtones,

Question

Qi.(10') In a group of households, 60% of the households live in New Temtones, 30% of the households live in Kowloon and 10% of the households live in Hong Kong Island, 50% of the households live in New Territories have more than one child, 30% of the households live in Kowloon have more than one child and 10% of the households live in Hong Kong Island have more than one child. A household is randomly selected from the group. Given that the household has more than one child, find the probability that the household lives in New Territories

Explanation / Answer

Let

N = New Teritories

K = Kowloon

H = Hong Kong Island

Given:
P(N) = 0.60

P(K) = 0.30

P(H) = 0.10

Let

A = have more than one child.

So,

P(NA) = 0.60 X 0.50 = 0.30

P(KA) = 0.30 X0.30 = 0.09

P(HA) = 0.10 X 0.10 = 0.01

So,

P(A) = P(have more than one child)= 0.30 + 0.09 + 0.01 = 0.40

To find P(N/A) :
By Multiplication Theorem:
P(N/A) = P(NA)/P(A)

           = 0.30/0.40 = 0.75

So,

Answr is:

0.75

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