document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1019075>Question 1019075</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You have a pot with 100 balls. 20 of them are red, 50 are blue and 30 are green. You decide to draw 5 balls from the pot without replacement (i.e. you don't put a ball back in the pot once it has been taken out). What is the probability of drawing five blue balls?\r<BR>\n" );
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document.write( "Give your answer to 3 decimal places. </SPAN>\n" );
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document.write( "Question:<BR>\n" );
document.write( "You have a pot with 100 balls. 20 of them are red, 50 are blue and 30 are green. You decide to draw 5 balls from the pot without replacement (i.e. you don't put a ball back in the pot once it has been taken out). What is the probability of drawing five blue balls?<BR>\n" );
document.write( "Give your answer to 3 decimal places.<BR>\n" );
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document.write( "Solution:<BR>\n" );
document.write( "The probability of drawing 5 blue balls is given by the product rule, namely the probability of having success in all five steps is the product of the probabilities of success in each step.<BR>\n" );
document.write( "Step 1: P(B)=50/100<BR>\n" );
document.write( "Step 2: P(B)=49/99   (49 blue balls left out of 99 remaining, i.e. no replacement)<BR>\n" );
document.write( "Step 3: P(B)=48/98<BR>\n" );
document.write( "Step 4: P(B)=47/97<BR>\n" );
document.write( "Step 5: P(B)=46/96<BR>\n" );
document.write( "Now multiply together the probabilities of each step.<BR>\n" );
document.write( "P(BBBBB)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2850%2F100%29%2849%2F99%29%2848%2F98%29%2847%2F97%29%2846%2F96%29 ALIGN=MIDDLE  ALT=\"%2850%2F100%29%2849%2F99%29%2848%2F98%29%2847%2F97%29%2846%2F96%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1081%2F38412 ALIGN=MIDDLE  ALT=\"1081%2F38412\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=0.0281 (approximately)<BR>\n" );
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document.write( "This problem can also be solved using the Hypergeometric distribution, which gives <BR>\n" );
document.write( "P(BBBBB)=C(50,5)*C(50,0)/C(100,5)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1081%2F38412 ALIGN=MIDDLE  ALT=\"1081%2F38412\"   DISABLED_style= \"max-width:90%; height:auto;\" > as before.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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