Question

There are six cats and seven dogs in the local animal shelter. Four animals are chosen at random to visit a local school to educate the children on the great need for homes for these animals.
What is the probability that exactly two of the animals are cats?
What is the probability that at least one cat is chosen?

Answer 1

two cats, and therefore 2 dogs
quick answer is \[\huge \frac{\binom{6}{2}\binom{7}{2}}{\binom{13}{4}}\]

Answer 2

where \(\binom{6}{2}\) means "six choose 2"

Answer 3

you familar with that notation? some people write \(_6C_2\)

Answer 4

I use 6C2 but I think I understand yours

Answer 5

So by doing that I get 0.44 or 44% right?

Answer 6

That's the chance of there being two cats ?

Answer 7

i don't know, i didn't do it
you want me to check?

Answer 8

I think I got it, I did it twice a couple of ways and ended up with the same answer. It's hypergeometric distribution right? So to do the second part of the question I would do the same thing? Or would I have to change something?

Answer 9

yeah looks good
http://www.wolframalpha.com/input/?i=%2815*21%29%2F%2813+choose+4%29

Answer 10

second one is easier

Answer 11

compute the probability that all are dogs, subtract that from 1

Answer 12

So do 7C4 then subtract it from 1?

Answer 13

\[1-\frac{\binom{7}{4}}{\binom{13}{4}}\]

Answer 14

ohhhhhhh

Answer 15

When I did that I got 95.01% chance of at least one cat, would you mind double checking that one for me??

Answer 16

sorry 95.10%

Answer 17

i get the same thing
http://www.wolframalpha.com/input/?i=1-%287+choose+4%29%2F%2813+choose+4%29