A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 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.

  • This Question is Closed
  1. ZeHanz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  5. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

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
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.