document.write( "Question 1139068: A red dye and a green die are rolled as a pair. Let E be the event that \"the red die shows a 2\" and let F be the event that \"the sum of the numbers is 8.\" Are the events E and F independent? \n" ); document.write( "

Algebra.Com's Answer #756855 by ikleyn(52798) $\"\"$ $\"About$

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\n" ); document.write( "A red $\"highlight%28cross%28dye%29%29\"$ die and a green die are rolled as a pair.
\n" ); document.write( "Let E be the event that \"the red die shows a 2\" and let F be the event that \"the sum of the numbers is 8.\"
\n" ); document.write( "Are the events E and F independent?
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document.write( "The probability of event E  is  P(E) = .\r\n" );
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document.write( "The probability of event F  is  P(F) =  \r\n" );
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document.write( "    (since there are 5 pairs with the sum 8  (2,6), (3,5), (4,4), (5,3), (6,2)  among 36 possible outcomes - pairs (m,n), \r\n" );
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document.write( "    where m and n are integers between 1 and 6 inclusively).\r\n" );
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document.write( "The probability of event  (E & F)  is  P(E & F) = \r\n" );
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document.write( "    (since there is only one pair (red2, green6) with the sum 8 among 36 possible outcomes - pairs (m,n), \r\n" );
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document.write( "    where m and n are integers between 1 and 6 inclusively).\r\n" );
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document.write( "Now,  the product  P(E)*P(F)  is equal to   = ,   while  P(E & F) = .\r\n" );
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document.write( "As you see,   P(E)*P(F)  is not equal to  P(E & F),  therefore events E and F are not independent.     ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "On usage the words \"die\" and \"dice\" see this nice article from the Internet\r
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\n" ); document.write( "\n" ); document.write( "https://www.grammarly.com/blog/dice-die/\r
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\n" ); document.write( "\n" ); document.write( "https://www.grammarly.com/blog/dice-die/'\r
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