Black bears and tan-colored bears catching salmon in Alaska

405 Views Asked by At

One of popular tourist attractions in Alaska is watching black bears catch salmon swimming upstream to spawn. Not all "black" bears are black, though- some are tan-colored. Suppose that 6 black bears and 3 tan-colored bears are working the rapids of a salmon stream. Over the course of an hour, 6 different bears are sighted. What is the probability that those 6 include at least twice as many black bears as tan-colored bears?

Attempt: I need to use the hypergeometric distribution. That is P(K chosen) = [r_C_k * w_C_(n-k)]/N_C_n. There are 6 black bears and 3 tan for a total of 9 bears. Thus, N = 9. Please can someone please help me? I don't understand this problem. Thank you.

1

There are 1 best solutions below

3
On

This does not happen when the sample of 6 sighted bears includes $____$ black bears and $____$ tan-colored bears. There are $k=$ $____$ ways to compose such a sample of 6 bears from the 9 in the stream, and $\ell=$ $____$ ways to compose any sample of 6 bears from the 9 in the stream hence the desired probability is $1-(k/\ell)=$ $____$.