document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191771>Question 1191771</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the game of Yahtzee, five dice are thrown. On such a roll, Pat gets a 4,4,4,3, and 5. The rules allow her two more chances to roll any subset of the 5 dice. Hoping for a Yahtzee, she saves the first three dice and rerolls the dice that had a 3 and 5. Her strategy is:\r<BR>\n" );
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document.write( "a) if her 2nd roll is 4 and 4, then she stops and has achieved a Yahtzee\r<BR>\n" );
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document.write( "b) if her 2nd roll has a 4 and something else, she will keep the 4 and roll the other die one more time trying to get a 4\r<BR>\n" );
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document.write( "c) if her 2nd roll has no 4's then she will reroll those two dice one more time, trying to get both dice to be a 4\r<BR>\n" );
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document.write( "What is the probability she will end up with a successful Yahtzee? \r<BR>\n" );
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document.write( "Sorry for the long question, I have no idea where to start and it's overwhelming... Thank you to whoever finds the time to help me! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #823608 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=823608\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "She gets a Yahtzee in any of three ways; calculate the probability in each case.<br><BR>\n" );
document.write( "(1) both dice show 4 on the second roll<br><BR>\n" );
document.write( "P(4) on each die is 1/6, so P(4 on both dice) is (1/6)(1/6)=1/36<br><BR>\n" );
document.write( "(2) one die shows 4 on the second roll and the remaining one die shows 4 on the third roll<br><BR>\n" );
document.write( "P(4) on each die is 1/6; P(not 4) on each die is 5/6.<BR>\n" );
document.write( "Either the first die can be a 4 and the other not, or the other way around.<BR>\n" );
document.write( "P(4 then not 4) = (1/6)(5/6) = 5/36<BR>\n" );
document.write( "P(not 4 then 4) = (5/6)(1/6) = 5/36<BR>\n" );
document.write( "P(1 of 2 dice showing 4) = 10/36 = 5/18<BR>\n" );
document.write( "P(4 on third roll) = 1/6<BR>\n" );
document.write( "P(Yahtzee with one 4 on second roll and one on third roll) = (5/18)(1/6) = 5/108<br><BR>\n" );
document.write( "(3) neither die shows 4 on the second roll and both show 4 on the third roll.<br><BR>\n" );
document.write( "P(neither die shows 4 on second roll) = (5/6)(5/6) = 25/36<BR>\n" );
document.write( "P(both dice show 4 on third roll) = (1/6)(1/6) = 1/36<BR>\n" );
document.write( "P(Yahtzee with two 4's on third roll - (25/36)(1/36) = 25/1296<br><BR>\n" );
document.write( "P(Yahtzee with three 4's on first roll) = (1/36)+(5/108)+(25/1296) = (36/1296)+(60/1296)+(25/1296) = 121/1296<br><BR>\n" );
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