document.write( "Question 1195176: You roll two six-sided fair dice.\r
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\n" ); document.write( "\n" ); document.write( "b. Let B be the event that the sum of the two dice is at most 7.
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\n" ); document.write( "\n" ); document.write( "c. Are A and B mutually exclusive events?\r
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Algebra.Com's Answer #827578 by ikleyn(52788) $\"\"$ $\"About$

You can put this solution on YOUR website!
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One and ONLY ONE problem/question per post.

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\n" ); document.write( "\n" ); document.write( "But 4 (four) questions in one post is FAR BEYOND the BOUNDS\r
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\n" ); document.write( "\n" ); document.write( "that a reasonable person in healthy mind may allow to himself.\r
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\n" ); document.write( "\n" ); document.write( " Below is my addition, which I made after reading the post by @greenestamps.\r
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\n" ); document.write( "\n" ); document.write( "In the post by @greenestamps, the reasoning, related to question (d), is INCORRECT, and his answer is WRONG.\r
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document.write( "To determine, if events A and B are independent, you should check if P(A ∩ B) = P(A)*P(B).\r\n" );
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document.write( "     +-------------------------------------------------------------------+\r\n" );
document.write( "     |  If the equality is valid, the events are independent;            |\r\n" );
document.write( "     |  if the equality is not valid, the events are not independent.    |\r\n" );
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document.write( "Event A has the following 6 outcomes :  \r\n" );
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document.write( "    (3,1), (3,3), (3,5), (4,1), (4,3), (4,5).   \r\n" );
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document.write( "Therefore, the probability P(A) is   = .\r\n" );
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document.write( "Event B has 21 outcomes.  Therefore, the probability P(B) =  = .\r\n" );
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document.write( "Event (A ∩ B) has the following 4 outcomes :  (3,1), (3,3), (4,1), (4,3).            \r\n" );
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document.write( "Therefore,  P(A ∩ B)  is   = .\r\n" );
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document.write( "        But  P(A)*P(B) =  =   is not equal to  P(A ∩ B) = .\r\n" );
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document.write( "It shows/proves that the events A and B are not independent.\r\n" );
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document.write( "ANSWER to question (d):  the events A and B are not independent.\r\n" );
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Two lessons to learn from my post :

\r
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\n" ); document.write( "\n" ); document.write( "         (2)   @greenestamps calls my right response as idiotic, but sells you his wrong response as correct.\r
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\n" ); document.write( "         From it, make your own conclusions.\r
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\n" ); document.write( "\n" ); document.write( "Wow, @greenestamps, how much expression in your last invectives (!)\r
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\n" ); document.write( "\n" ); document.write( "One can immediately see an educated intelligent person, even from afar.\r
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\n" ); document.write( "\n" ); document.write( "Your vocabulary is much wider than my - I even don't know such English words (!)\r
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