In a litter of seven kittens, three are female. You pick three kittens at random. Create a probability model for the number of female kittens you get.

Question

anonymous · Answer

This is the model given in the answers section.

anonymous · Answer

I just want to know how they arrived at those fractions (x/35).

anonymous · Answer

I am aware that all the probabilities must add up to 1, but how did they end up with those specific fractions?

anonymous · Answer

Probability of picking 0 kittens out of three =(4/7)(3/6)(2/5)= picked white 3 times
Probability of picking 1 kitten out of three tries: 
(4/7)(3/6)(3/5)   got female on third try
(4/7)(3/6)(3/5) got female on second try
(3/7)((4/6)(3/5) got female on third try
These are selections without replacement, changing numerator and denominator.
etc.

Must be an easier way!

anonymous · Answer

I think there might be a way to figure this out using the TI-84's nCr command, but I'm not sure. I'm kinda confused on what they did.

anonymous · Answer

The problem I have is that these are selected without replacement, so the denominator always goes down and sometimes the numerator does also.

anonymous · Answer

Nobody knows.

kropot72 · Answer

$$P(0\ kitten)=\frac{3C0\times4C3}{7C3}$$
$$P(1\ kitten)=\frac{3C1\times4C2}{7C3}$$
$$P(2\ kittens)=\frac{3C2\times4C1}{7C3}$$
$$P(3\ kittens)=\frac{3C3\times4C0}{7C3}$$