Respuesta :
Answer:
the probability is 0.051 (5.1%)
Step-by-step explanation:
since the fact that person owns a dog independently of the behaviour of the other people , then the random variable X= number of people that owns a dog from 10 interviewed , follows a binomial distribution .
P(X=x) = C (n,x)* p^x * (1-p)^(n-x)
where
n= sample size = 10
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) = C (n-1,x-1)* p^x * (1-p)^(n-x)
= C (9,4)* 0.3^5 * 0.7^(10-5) = 0.051 (5.1%)
therefore the probability is 0.051 (5.1%)
Answer:
- The probability that the tenth person randomly interviewed in that city is the fifth one to own a dog = [tex]0.051[/tex]
Step-by-step explanation:
Probability of owning a dog = 0.3
Since the tenth person randomly interviewed is the fifth one to own a dog, it means four of the nine persons interviewed has a dog.
Probability of 4 out of 9 person has a dog
[tex]= ^9C_4 (0.3)^4(0.7)^5\\\\= 126 (0.3)^4(0.7)^5\\\\= 0.17[/tex]
Therefore, probability the tenth person interviewed is the fifth to own a dog
[tex]= 0.17 * 0.3\\\\= 0.051[/tex]
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