document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1025792>Question 1025792</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a certain city district, the need for money to buy drugs is given as the reason for 65% of all thefts. What is the probability that exactly 2 of the next 4 theft cases reported in this district resulted from the need for money to buy drugs? 	 </SPAN>\n" );
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document.write( "Question:<BR>\n" );
document.write( "In a certain city district, the need for money to buy drugs is given as the reason for 65% of all thefts. What is the probability that exactly 2 of the next 4 theft cases reported in this district resulted from the need for money to buy drugs? 	<BR>\n" );
document.write( " <BR>\n" );
document.write( "Solution:<BR>\n" );
document.write( "We know that the experiment consists of 4 Bernoulli (true or false) trials, with a constant probability of 0.65.  We further assume that the (next) cases are random and independent of each other.  This way, the situation can be modelled by the binomial distribution, having<BR>\n" );
document.write( "p=0.65,<BR>\n" );
document.write( "n=4<BR>\n" );
document.write( "k=2 (number of \"successes\", meaning drug related motive).<BR>\n" );
document.write( "with a probability of<BR>\n" );
document.write( "P(k,n,p)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28n%2Ck%29%2Ap%5Ek%2A%281-p%29%5E%28n-k%29 ALIGN=MIDDLE  ALT=\"C%28n%2Ck%29%2Ap%5Ek%2A%281-p%29%5E%28n-k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where <BR>\n" );
document.write( "C(n,k)=n!/(k!(n-k)!)<BR>\n" );
document.write( " <BR>\n" );
document.write( "Substituting values,<BR>\n" );
document.write( "P(2,4,0.65)<BR>\n" );
document.write( "=6*0.4225*0.1225<BR>\n" );
document.write( "=0.3105375<BR>\n" );
document.write( "=0.311 (rounded to 3 sig. figures) </SPAN>\n" );
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