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;
![P(X=r)=\binom{n}{r} \times p^{r}\times (1-p)^{n-r}; x = 0,1,2,3,.....](https://tex.z-dn.net/?f=P%28X%3Dr%29%3D%5Cbinom%7Bn%7D%7Br%7D%20%5Ctimes%20p%5E%7Br%7D%5Ctimes%20%281-p%29%5E%7Bn-r%7D%3B%20x%20%3D%200%2C1%2C2%2C3%2C.....)
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 = <u><em>Number of people who have a do</em></u><em>g</em>
SO, X ~ Binom(n = 5, p = 0.60)
Now, probability that at least 2 of them have a dog is given by = P(X
2)
P(X
2) = 1 - P(X < 2)
= 1 - P(X = 0) - P(X = 1)
=
=
= 1 - 0.01024 - 0.0768
= <u>0.913</u>
Therefore, probability that at least 2 of them have a dog is 0.913.