Respuesta :
Answer:
Probability that at least 2 of them have a dog is 0.913.
Step-by-step explanation:
We are given that according to a survey 60% of people have a dog.
Also, 5 people are selected randomly.
The above situation can be represented through binomial distribution;
[tex]P(X=r)=\binom{n}{r} \times p^{r}\times (1-p)^{n-r}; x = 0,1,2,3,.....[/tex]
where, n = number of trials (samples) taken = 5 people
r = number of success
p = probability of success which in our question is probability
that people have a dog, i.e; p = 60%
Let X = Number of people who have a dog
SO, X ~ Binom(n = 5, p = 0.60)
Now, probability that at least 2 of them have a dog is given by = P(X [tex]\geq[/tex] 2)
P(X [tex]\geq[/tex] 2) = 1 - P(X < 2)
= 1 - P(X = 0) - P(X = 1)
= [tex]1-\binom{5}{0} \times 0.60^{0}\times (1-0.60)^{5-0}-\binom{5}{1} \times 0.60^{1}\times (1-0.60)^{5-1}[/tex]
= [tex]1-(1 \times 1\times 0.40^{5})-(5\times 0.60^{1}\times 0.40^{4})[/tex]
= 1 - 0.01024 - 0.0768
= 0.913
Therefore, probability that at least 2 of them have a dog is 0.913.
