Question

A houseowner plants 6 seeds which he selects at random from a box containing 5 tulip seeds and 4 narcissus seeds. What's the probability of him planting 2 narcissus and 4 tulip seeds?

It is supposedly to be solved using hypergeometric distribution, but I'm not getting the correct result (5/14 chance).

Answer 1

number of ways to choose 6 out of 9 is \(\binom{9}{6}\) for your denominator
you want 2 out of 4 narcissus, that is \(\binom{4}{2}\) and 4 out of 5 tulips whichis \(\binom{5}{4}\) so you need to compute
\[\frac{\dbinom{4}{2}\dbinom{5}{4}}{\dbinom{9}{6}}\]

Answer 2

computation is easy enough in this case because \(\binom{4}{2}=12\), \(\binom{5}{4}=5\) pretty much from your eyeballs. then \(\binom{9}{6}=84\) from a calculator

Answer 3

hmm i get \(\frac{5}{7}\)

Answer 4

Thank you very much, I was quite lost, since I was expecting a sum somewhere in the procedure, but ends up it's pretty simple!. It works out just fine to 5/14 in my calculator.

Answer 5

i am sticking with my answer

Answer 6

oh duh, \(\binom{4}{2}=6!!\)

Answer 7

you beat me to it haha

Answer 8

yes you are right

Answer 9

Thanks!