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

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.

Answer 2

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.