The probability of the tenth person randomly interviewed in that city is the sixth one to own a dog is 0.051 (5.1%).
p= probability that a person owns a dog = 0.3
x= number of people found that owns a dog = 5
C(n,x) = combinations of 5 persons who owns a dog from 10 interviewed ( number of times we can observe 5 people from 10 owning a dog)
For our case we know that the tenth person has a dog , then considering that constraint the number of times observed must be modified and is equal to the number of times we can observe 4 people out of 9 that has a dog ( since we know already that the tenth will be a person who owns a dog)
Therefore
P(tenth person is the fifth one to own a dog) = [tex]P(X=x) = C (n,x)\times p^x \times (1-p)^{(n-x)}[/tex]
= [tex]C (9,4) \times 0.3^5 \times {0.7^{(10-5)} = 0.051[/tex]
Therefore the probability is 0.051 (5.1%)
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