Discerning Difference Between Discrete Random Variable Distributions Okay, so I have a few example that would follow Discrete random variable distributions, but I am having a hard time understanding when to use which distribution.

$1.$ You are in possession of a fake ID that gets
  you into a club $20%$ percent  of the time. Each attempt
  is independent of other attempts. Let
  $F$ denote the number of clubs that you fail to
  get into prior to getting into $2$ clubs. How is
  $F$ distributed?
$2.$ A bowl contains $6$ green, $5$ yellow, $4$ orange, $3$
  red, $2$ blue, and $1$ brown skittles. Randomly
  grab five skittles from the bowl. Let $R$ denote
  the number of red skittles you grab. How is $R$
  distributed?
$3.$ Play $50$ rounds of roulette always betting on
  black. Let $L$ denote the number of times you
  lose. A roulette table has $18$ black spaces, $18$
  red spaces, and $2$ green spaces. All $38$ spaces
  have equal size. You win if a ball lands on a
  black space. You lose if the ball lands on a
  red or green space. How is $L$ distributed?
$4.$ A family is going to make babies until they
  have three girls. Let $T$ denote the total
  number of children in the family. How is $T$
  distributed?

My attempts: $1.$ Negative Binomial (Because we are looking for $2$ successes and want to know number of trials until then.)
$2.$ I am fairly certain this is a hypergeometric distribution. (My question mainly pertains to the other distributions)
$3.$ I believe that this distribution is a regular binomial distribution (Looking for $k$ successes)
$4.$ I am unsure on this one, I lean towards Negative Binomial as well, but am not sure. It seems similar to $1.$ to me.
I am struggling to understand when a certain distribution applies and when it doesn't. For example, numbers $1.$, $3.$, and $4.$ all seem to be very close to me. 
 A: 
$1.$ You are in possession of a fake ID that gets you into a club $20%$ percent  of the time. Each attempt is independent of other attempts. Let $F$ denote the number of clubs that you fail to get into prior to getting into $2$ clubs. How is $F$ distributed?

$F$ is the count for "successes" before the second "failure" in an indefinite sequence of independent and identically distributed Bernoulli trials with given "success" rate.  (Note: a "success" here is "not getting into the club".† )
This is indeed a negative binomial distribution with parameters $r=2,$ and $p=0.80$. 

$2.$ A bowl contains $6$ green, $5$ yellow, $4$ orange, $3$ red, $2$ blue, and $1$ brown skittles. Randomly grab five skittles from the bowl. Let $R$ denote
  the number of red skittles you grab. How is $R$ distributed?

$R$ is the count of successes selected in a sample of known size selected from a population of known size containing a known amount of successes.
This is indeed a hypergeometric distribution whith parameters of $N=16$, $K=3$, and $n=5$.

$3.$ Play $50$ rounds of roulette always betting on black. Let $L$ denote the number of times you lose. A roulette table has $18$ black spaces, $18$ red spaces, and $2$ green spaces. All $38$ spaces have equal size. You win if a ball lands on a black space. You lose if the ball lands on a red or green space. How is $L$ distributed?

$L$ is the count of "successes" (a loss) in a definite sequence of iid Bernoulli trials with calculatable "success" rate.
This is indeed a binomial distribution. What are the parameters?

$4.$ A family is going to make babies until they have three girls. Let $T$ denote the total number of children in the family. How is $T$ distributed?

$T$ is the count of trials until three "failures"† in an indefinite sequence of iid Bernouli trials with a "success" rate you have to assume.  
Now $T{-}3$ has a negative binomial distribution, so $T$ itself has a shifted negative binomial distribution.
( Of course, some texts will call this a negative binomial and call that of $F$ the shifted distribution.   So it always pays to be clarify exactly what is being counted. )

† For centuries Mathematicians have been annoyed by the "success" and "failure" terminiology, but haven't come up with anything better because, meh.
A: 4.negative binomial
3.binomial
I think and 
1.) is negative binomial.
As I remember for 
2.)  you must specify the number of g,y,r,o,b
A: Unfortunately the term "negative binomial" is used in two conflicting senses. It is sometimes taken to mean the distribution of the number of failures before a specified number of successes (so that it can be $0,1,2,3,\ldots$) and sometimes to mean the number of trials needed to get the specifited number of successes (so that it can be $r,r+1,r+2,r+3,\ldots$, where $r$ is that specified number). #1 and #4 have negative binomial distributions according to the first and second senses respectively.
#2 is hypergeometric and #3 is binomial.
