document.write( "Question 981805: 23​% of a certain​ country's voters think that it is too easy to vote in their country. You randomly select 12 likely voters. Find the probability that the number of likely voters who think that it is too easy to vote is​ (a) exactly​ three, (b) at least​ four, (c) less than eight. \n" ); document.write( "
Algebra.Com's Answer #602737 by Boreal(15235)\"\" \"About 
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exactly 3
\n" ); document.write( "12C3 (0.23)^3(0.77)^9=0.2547
\n" ); document.write( "At least 4 means all others except 0,1,2,3.
\n" ); document.write( "We know what 3 is
\n" ); document.write( "for 2: 12C2*(0.23)^2*(0.77)^10=0.2558
\n" ); document.write( "for 1: 12*.23*.77^11=0.1557
\n" ); document.write( "for 0: .77^12=0.0434
\n" ); document.write( "Those 4 sum to 0.7096\r
\n" ); document.write( "\n" ); document.write( "At least 4 is 1-0.7096, since it is the complement. It is 0.2904.\r
\n" ); document.write( "\n" ); document.write( "For less than 8
\n" ); document.write( "probability of 4 is 12C4(0.23)^4(0.77)^8=0.1712
\n" ); document.write( "probability of 5=12C5(0.23)^5(0.77)^7=0.0818
\n" ); document.write( "probability of 6=12C6(0.23)^6*(0.77)^6=0.0285
\n" ); document.write( "probability of 7=12C7(0.23)^7(0.77)^5=0.0073
\n" ); document.write( "These 4 sum to 0.2888
\n" ); document.write( "The other 4 sum to 0.7096
\n" ); document.write( "The probability it is less than 8 is their sum or 0.9984. \n" ); document.write( "
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