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Suppose we select two students at random from the class of fifteen. What is the probability that both students chosen have less then 100 books at home?

Data provided is the amount of books each student has at home. There are 6 out of the 15 students that have less than 100 books:

33, 47, 48, 52, 56, 66, 173, 186, 251, 300, 323, 417, 450, 1280, 2000

I tried doing 6/15 x 5/14 = 30/210 or a 14% chance. Is this correct?

Thank you!

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  • $\begingroup$ @MarcusM with "order matters", the order of what are you referring to? $\endgroup$
    – user126540
    Jul 31, 2015 at 2:53
  • $\begingroup$ @MarcusM Sorry that's just how the question was worded but I am sure of it that the order doesn't matter $\endgroup$
    – coopwatts
    Jul 31, 2015 at 2:55
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    $\begingroup$ @MarcusM The answer does not imply that order matters. If you compute it with binomial coefficients instead you'll get the same answer. $\endgroup$
    – Matt Samuel
    Jul 31, 2015 at 2:57
  • $\begingroup$ Oops! My bad. The $2$'s cancel. $\endgroup$
    – Marcus M
    Jul 31, 2015 at 3:08

1 Answer 1

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$L_1$ is the event that the first student has less than $100$ books,
$L_2$ is the event that the second has less than $100$ books.

$$P(L_1\cap L_2) = P(L_1)\cdot P(L_2\ |\ L_1)$$ $$= \frac{6}{15}\cdot \frac{5}{14}$$

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