document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1185443>Question 1185443</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3.	Suppose that you roll a fair die 5 times. What are the odds that you roll\r<BR>\n" );
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document.write( "a) Exactly 4 sixes \r<BR>\n" );
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document.write( "b) At least 4 sixes. <BR>\n" );
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document.write( "a) exactly 4 sixes<br><BR>\n" );
document.write( "The probability of a 6 on each roll is 1/6; the probability of any other outcome is 5/6.<br><BR>\n" );
document.write( "The number of orders in which you can get exactly 4 sixes in 5 rolls is C(5,4).<br><BR>\n" );
document.write( "P(4 sixes in 5 rolls) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%285%2C4%29%28%281%2F6%29%5E4%29%28%285%2F6%29%5E1%29=5%285%2F6%5E5%29=25%2F6%5E5=25%2F7776 ALIGN=MIDDLE  ALT=\"C%285%2C4%29%28%281%2F6%29%5E4%29%28%285%2F6%29%5E1%29=5%285%2F6%5E5%29=25%2F6%5E5=25%2F7776\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: 25/7776<br><BR>\n" );
document.write( "b) at least 4 sixes<br><BR>\n" );
document.write( "To the answer for part a, add the probability of getting sixes on all 5 rolls.<br><BR>\n" );
document.write( "P(5 sixes on 5 rolls) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F6%29%5E5=1%2F7776 ALIGN=MIDDLE  ALT=\"%281%2F6%29%5E5=1%2F7776\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: 26/7776 (simplify if required)<br><BR>\n" );
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