document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1182323>Question 1182323</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Using the binomial distribution, find the probability that (i) Three successes            [10]<BR>\n" );
document.write( "            in 8 trials when P = 0.4. (ii) Two or fewer successes in 9 trials when P = 0.6<BR>\n" );
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document.write( "Part (i)\r<BR>\n" );
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document.write( "n = 8 = number of trials<BR>\n" );
document.write( "p = 0.4 = probability of success<BR>\n" );
document.write( "k = 3 = number of successes that we want\r<BR>\n" );
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document.write( "Binomial probability formula<BR>\n" );
document.write( "P(k) = (n C k)*(p)^k*(1-p)^(n-k)<BR>\n" );
document.write( "P(3) = (8 C 3)*(0.4)^3*(1-0.4)^(8-3)<BR>\n" );
document.write( "P(3) = 56*(0.4)^3*(1-0.4)^(8-3)<BR>\n" );
document.write( "P(3) = <font color=red>0.27869184</font><BR>\n" );
document.write( "This reprsents the probability of getting exactly 3 successes. The decimal value is exact.\r<BR>\n" );
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document.write( "Note: the n C k refers to the combination formula <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large _n C _r = \frac{n!}{r!*(n-r)!}\"> but you replace r with k and you get the same idea.\r<BR>\n" );
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document.write( "<font color=red>Answer: 0.27869184</font> (round this however you need to)\r<BR>\n" );
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document.write( "================================================\r<BR>\n" );
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document.write( "Part (ii)\r<BR>\n" );
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document.write( "Use the formula from part (i) to find the following<BR>\n" );
document.write( "P(0) = 0.000262144<BR>\n" );
document.write( "P(1) = 0.003538944<BR>\n" );
document.write( "P(2) = 0.021233664<BR>\n" );
document.write( "where n = 9 and p = 0.6 this time (k will range from 0 to 2 as shown above)\r<BR>\n" );
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document.write( "Add up those results to get<BR>\n" );
document.write( "0.000262144 + 0.003538944 + 0.021233664 = <font color=red>0.025034752</font> \r<BR>\n" );
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document.write( "This represents the probability of getting 2 or fewer (ie at most 2) successes. This decimal value is exact.\r<BR>\n" );
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document.write( "<font color=red>Answer: 0.025034752</font> (round this however you need to)<BR>\n" );
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