## anonymous one year ago find the probability of probability of randomly selecting three science books and four history books from a box containing five science books and six history books.

1. ZeHanz

This is a counting problem. It has to do with the hypergeometric distribution. I don't know if you are familaiar with that, so here I go: You ramdomly pick a number of items (7) out of a total of 11 items. There are two kinds of items: s(cience) and h(istory) books. If X is the number of science books in the 7 books you select, then: $P(X=x)=\frac{ \left(\begin{matrix}x \\ a\end{matrix}\right)\cdot \left(\begin{matrix}n-x \\ b\end{matrix}\right) }{ \left(\begin{matrix}N \\ n\end{matrix}\right) }$

2. ZeHanz

Now this is less scary than you might think! N = total no of items (11) n = sample size (7) a = no of items of the first kind (5 science books) b = no of items of the second kind (6 history books) x = no of items of first kind in sample (3 science books) You want 3 science books and 4 history books, so you can compute the probability as follows:

3. ZeHanz

Sorry, I should have put the a and b on the top in the formula!! The probability is:$P(X=3)=\frac{ \left(\begin{matrix}5 \\ 3\end{matrix}\right)\cdot \left(\begin{matrix}6 \\ 4\end{matrix}\right) }{ \left(\begin{matrix}11 \\ 7\end{matrix}\right) }$

4. ZeHanz

I hope you can follow my explaining! Also, you still have to calculate the binomial coefficients in the formula.