document.write( "Question 1158563: Let X represent the difference between the number of heads and the number of tails when a coin is tossed 33 times. Then P(X=3)= \n" ); document.write( "

Algebra.Com's Answer #781517 by ikleyn(52858) $\"\"$ $\"About$

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\n" ); document.write( "Let X $\"highlight%28cross%28represent%29%29\"$ represents the difference between the number of heads and the number of tails
\n" ); document.write( "when a coin is tossed 33 times. Then P(X=3)=
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document.write( "In this problem, the sum  Heads+Tails  is 33,  while the difference Heads-Tails = 3.\r\n" );
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document.write( "It immediately follows that Heads = 18, Tails = 15.\r\n" );
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document.write( "Therefore, the event X= 3 is EQUIVALENT to event Tails = 15.\r\n" );
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document.write( "Now, P(Tails=15) is (use the formula of probability for the Binomial distribution)\r\n" );
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document.write( "    P(Tails=15) =  = BINOM.DIST(15, 33, 0.5, FALSE) = 0.120741.    ANSWER\r\n" );
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document.write( "I used the standard EXCEL function to calculate the binomial distribution probability.\r\n" );
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document.write( "        Its second parameter is the \"number of trials n\"           (n= 33 in this case);  \r\n" );
document.write( "        the first parameter is the \"number of successful trials\"   (k= 15 in this case);\r\n" );
document.write( "        third parameter is \"the probability of success in each one single trial\"  (p= 0.5 in this case); and \r\n" );
document.write( "        the fourth parameter says if you want calculate a single addend or the sum of addends (the single addend in this case).\r\n" );
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document.write( "    Input  \"=BINOM.DIST(15, 33, 0.5, FALSE)\" into any MS Excel cell in your computer and press enter to get the answer P = 0.120741 immediately.\r\n" );
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document.write( "    On Excel function BINOM.DIST, see its description everywhere, for example\r\n" );
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document.write( "    https://support.office.com/en-us/article/binom-dist-function-c5ae37b6-f39c-4be2-94c2-509a1480770c\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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