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For the events of $A$ and $B$, probabilites are $\Bbb P(A) = 3/11$ and $\Bbb P(B) = 4/11$. Define the $\Bbb P(A \cap B )$ if:

a) $\Bbb P(A \cup B) = 6/11$.

b) events are indenpendent

I have done a task, and it's following

$\Bbb P(A \cup B) = \Bbb P(A) + \Bbb P(B) - \Bbb P(A \cap B ) = 1/11\;.$

However I don't know how to solve b task. I need your help.

Thanks in advance.

2 Answers 2

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To say that $A$ and $B$ are independent is to say that $\Bbb P(A\cap B)=\Bbb P(A)\Bbb P(B)$.

By the way, it’s not correct to write

$\Bbb P(A\cup B)=\Bbb P(A)+\Bbb P(B)-\Bbb P(A\cap B)=1/11$;

what you mean is that $\Bbb P(A\cup B)=\Bbb P(A)+\Bbb P(B)-\Bbb P(A\cap B)$, so $\Bbb P(A\cap B)=1/11$.

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    Yes, I wanted to solve P( A intesection B), but I hurried up and wrote P( A union B)! What I did there was union, so I will fix it out now. Than$k$s for your help, @Brian M. Scott2012-07-02
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Independence means $P(A \cap B)=P(A) P(B)$ but $P(A) P(B)=3 \times 4/121 \approx 0.0991$ and you found $P(A \cap B)=1/11 \approx 0.09091$. Close but not equal, so not independent. Note the difference between $12/121$ vs $11/121$.

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    @BrianM.Scott As I reread the question your interpretation seems right. The problem is to calculate P(A interesection B) under 2 different scenarios. In the first case it would be 1/11 and in the second 12/121. My solution is to the problem are A and B independent if P(A)=3/11, P(B)=4/11 and P(AUB)=6/11.2012-07-02