Question

A veterinarian is using a new vaccine for cats. The vaccine has a 10% probability of causing side effects. In which distributions does the variable X have a binomial distribution? Select each correct answer.

_When the vaccine is given to multiple cats, X is the total number of cats that receive the vaccine
_When the vaccine is given to multiple cats, X is the number of cats that receive the vaccine until one of them has side effects.

_When the vaccine is given to three cats, X is the number of cats that have side effects.

_When the vaccine is given to six cats, X is the number of cats that do not have any side effects.

Answer 1

X follows the binomial distribution for the first experiment.
Denote the probabilities like this:
`p=0.1,q=1-p=0.9`
Then,

`P(X=n)=C_N^np^nq^(0.9)`
Wherein N is the total number of cats that receive vaccine.

Answer 2

Answer is option (1) When the vaccine is given to multiple cats, X is the total number of cats that receive the vaccine.

So for the random variable X ,where X is the total number of cats that receive the vaccine. We have the binomial distribution for

probability of causing side effect denoted by

p = 10% =0.1

and probability of not causing side effect denoted by

q = 1-0.1 =0.9

Then probability function for random variable X is

`P(X=n)={C}\binom{n}{0}p^(0.1)q^(0.9)`

where n is total number of cats.