A community for students.
Here's the question you clicked on:
 0 viewing
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.
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.

This Question is Closed

ZeHanz
 one year ago
Best ResponseYou've already chosen the best response.0This 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: \[P(X=x)=\frac{ \left(\begin{matrix}x \\ a\end{matrix}\right)\cdot \left(\begin{matrix}nx \\ b\end{matrix}\right) }{ \left(\begin{matrix}N \\ n\end{matrix}\right) }\]

ZeHanz
 one year ago
Best ResponseYou've already chosen the best response.0Now 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:

ZeHanz
 one year ago
Best ResponseYou've already chosen the best response.0Sorry, I should have put the a and b on the top in the formula!! The probability is:\[P(X=3)=\frac{ \left(\begin{matrix}5 \\ 3\end{matrix}\right)\cdot \left(\begin{matrix}6 \\ 4\end{matrix}\right) }{ \left(\begin{matrix}11 \\ 7\end{matrix}\right) }\]

ZeHanz
 one year ago
Best ResponseYou've already chosen the best response.0I hope you can follow my explaining! Also, you still have to calculate the binomial coefficients in the formula.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.