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Given Box contains 4 black cubes, 6 black spheres, 6 white cubes and x white spheres

P(black object) = 10/16+x

now i dont know what to do

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Hello, could you type in the question? This actually enhances the experience here, where we can search for your question with the words. Your question has a few key words eg. experiment, random, independent. Thanks! –  bryansis2010 Mar 13 '13 at 7:04
    
Just apply the definition of independence and solve for $x$. –  Macavity Mar 13 '13 at 7:04

2 Answers 2

For these events to be independent, the ratio of cubes to spheres has to be the same for white and black objects; equivalently the ratio of white objects to black objects has to be the same for cubes and spheres. This happens when $x=9$.

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Your experiment has

  • $4$ black cubes
  • $6$ black spheres
  • $6$ white cubes
  • $x$ white spheres
  • with a total of $16+x$ objects

$P(A) = P(\text{ cube drawn })\frac{10}{16+x}$ and $P(B) = P(\text{ black drawn })\frac{10}{16+x}$

If $A$ and $B$ are independent, we can apply the formula $P(A) \times P(B) = P(A\cap B)$

Now, realize that $P(A\cap B) = P(\text{ black cube drawn })= \frac{4}{16+x}$.

We can formulate the following equation:

$$ \frac{10}{16+x} \times \frac{10}{16+x} = \frac{4}{16+x} $$

Solving the equation, you should get $x=9$.

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