document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=65521>Question 65521</A>: <I><SPAN STYLE=\"word-break: break-all;\"> We had to make a probability game in Gr 12 Data Management. We now have to find out the probability of winning and the expected return. Mine was called Multiples. Here are the rules: <BR>\n" );
document.write( "· It costs $2 to play.<BR>\n" );
document.write( "· ace = 1, jack, queen, king = 10.<BR>\n" );
document.write( "· Roll the die.<BR>\n" );
document.write( "· If you roll a 1 you win automatically (because all numbers are multiples of 1)<BR>\n" );
document.write( "· If you roll any other number then pick the number of cards that corresponds to the number you rolled. (Example: if you roll a 4, choose 4 cards from the deck)<BR>\n" );
document.write( "· If all the cards add up to a multiple of the number you rolled then you win your bet back plus $1.<BR>\n" );
document.write( "· If all the cards add up to a multiple of the number you rolled, plus the number you rolled is one or more of the cards you selected, you win your bet back plus $4. (Example: if you roll a 4, there would have to be at least one 4 selected out of the 4 cards)<BR>\n" );
document.write( "· If your cards do not add to a multiple of the number you rolled, you lose. <BR>\n" );
document.write( "I don't get the probability Or the expected return. there must be a million cases because there are so many different sums of 2, 3, 4, 5, 6 you can get with a deck of 52 cards. Please help.:  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #46078 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=46078\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .SEE THE GUIDE LINE ANSWER BELOW.<BR>\n" );
document.write( "I AM CALLING IT AS GUIDELINE ANSWER AS IT IS LONG PROCEDURE IN A \"PROJECT WORK\" TYPE OF ASSIGNMENT<BR>\n" );
document.write( "AND YOU SHOULD BE ABLE TO CARRY FORWARD WITH THIS SYSTEMATIC METHOD OF APPROACH<BR>\n" );
document.write( "---------------------------------------------------------------------<BR>\n" );
document.write( "We had to make a probability game in Gr 12 Data Management. We now have to find out the probability of winning and the expected return. Mine was called Multiples. Here are the rules:<BR>\n" );
document.write( "· It costs $2 to play.<BR>\n" );
document.write( "OK<BR>\n" );
document.write( "· Roll the die.<BR>\n" );
document.write( "OK<BR>\n" );
document.write( "CASE 1<BR>\n" );
document.write( "· If you roll a 1 you win automatically (because all numbers are multiples of 1)<BR>\n" );
document.write( "OK·<BR>\n" );
document.write( "PROBABILITY = 1/6......EXPECTED TAKING = ???NOT GIVEN..LET ME TAKE IT AS 6.<BR>\n" );
document.write( "IF IT IS DIFFERENT , YOU CAN CORRECT EASILY.<BR>\n" );
document.write( "HENCE EXPECTED VALUE 1 = EV1 = 6*(1/6)=1.....................1<BR>\n" );
document.write( "CASE 2<BR>\n" );
document.write( "If you roll any other number then pick the number of cards that corresponds to the number you rolled. (Example: if you roll a 4, choose 4 cards from the deck)<BR>\n" );
document.write( "OK·<BR>\n" );
document.write( "THERE ARE 5 ALTERNATIVES HERE GIVING ROLLED NUMBER OF 2,3,4,5,6 EACH WITH AN EQUAL PROBABILITY OF 1/6..FIND EVS FOR EACH ALTERNATIVE AS SHOWN BELOW.<BR>\n" );
document.write( "ALTERNATIVE 1<BR>\n" );
document.write( "ROLLED NUMBER =2<BR>\n" );
document.write( "TOTAL COMBINATIONS OF TAKING 2 CARDS OUT OF 52..=52C2<BR>\n" );
document.write( "RANGE OF TOTALS FROM 2 CARDS =2 TO 20<BR>\n" );
document.write( "FOR SUCCESS TOTAL SHOULD EQUAL....2 OR 11 OR 20.....3 VARIANTS<BR>\n" );
document.write( "VARIANT 1<BR>\n" );
document.write( "TOTAL = 2<BR>\n" );
document.write( "POSSIBLE COMBINATION...2 ACES...TAKING 2 ACES OUT OF 4 ACES=4C2<BR>\n" );
document.write( "PROBABILITY = 4C2/52C2<BR>\n" );
document.write( "...OR....<BR>\n" );
document.write( "VARIANT 2<BR>\n" );
document.write( "TOTAL =11<BR>\n" );
document.write( "POSSIBLE COMBINATIONS = 1+10,2+9,3+8,4+7,5+6....<BR>\n" );
document.write( "1+10.......FROM 4 ACES & 10/J/Q/KINGS TOTALING 16 CARDS = 4C1*16C1<BR>\n" );
document.write( "PROBABILITY = 4C1*16C1/52C2<BR>\n" );
document.write( "SIMILARLY DO FOR 2+9,3+8,4+7,5+6<BR>\n" );
document.write( "VARIANT 3<BR>\n" );
document.write( "TOTAL =20<BR>\n" );
document.write( "POSSIBLE COMBINATIONS 10+10<BR>\n" );
document.write( "2 TENS/J/Q/K ..NUMBER OF SUCH CARDS=16...TAKING 2 OUT OF 16 CARDS= 16C2<BR>\n" );
document.write( "PROBABILITY = 16C2/52C2<BR>\n" );
document.write( "HENCE TOTAL PROBABILITY UNDER THIS ALTERNATIVE 1=<BR>\n" );
document.write( "(1/52C2)[4C2+4C1*16C1+.........+16C2]<BR>\n" );
document.write( "EXPECTED VALUE = (2+1)*(1/6)*(1/52C2)[4C2+4C1*16C1+............+16C2]..........2<BR>\n" );
document.write( "1/6 IS FOR THE PROBABILITY OF OCCURRENCE OF THIS ALTERNATIVE<BR>\n" );
document.write( "If all the cards add up to a multiple of the number you rolled then you win your bet back plus $1.<BR>\n" );
document.write( "OK<BR>\n" );
document.write( "ADD UP ALL EVS OBTAINED ABOVE FOR ALL THE VARIANTS UNDER EACH ALTERNATIVE AND ALSO THE TOTAL OF ALTERNATIVES.<BR>\n" );
document.write( "If all the cards add up to a multiple of the number you rolled, you win your bet back plus $4.\r<BR>\n" );
document.write( "\n" );
document.write( "\"I meant to say that, PLUS, if your number is included in those cards (ie. you roll a 4, there are 4 cards, but a 4 is one of the cards)\"<BR>\n" );
document.write( "OK<BR>\n" );
document.write( "THIS IS ALREADY INCLUDED AS A PART OF THE ABOVE CALCULATION.HENCE TAKE THOSE OUT SEPARATELY MULTIPLY WITH THE ADDITIONAL RETURN YOU GET (4-1=3 EXTRA)<BR>\n" );
document.write( "TO GET EV UNDER THIS CASE.<BR>\n" );
document.write( "If your cards do not add to a multiple of the number you rolled, you lose.<BR>\n" );
document.write( "OK<BR>\n" );
document.write( "THIS PROBABILITY IS 1- TOTAL YOU GOT ABOVE WITH EV OF ZERO.<BR>\n" );
document.write( "=============================================================<BR>\n" );
document.write( "NOW ADD UP ALL THE EVS YOU GOT ABOVE TO GET THE TOTAL EV!!<BR>\n" );
document.write( "MERRY X'MAS AND HAPPY NEW YEAR WITH THIS PROJECT!!!AND MANY MORE!!!!<BR>\n" );
document.write( "YOU THINK I AM CRUEL? ANY WAY MY BEST DEFENSE OR HOPE IS THAT YOU WONT OPEN TILL THE DAWN OF THE DAY AFTER NEW YEAR!!!!!!<BR>\n" );
document.write( "I don't get the probability. there must be a million cases because there are so many different sums of 2, 3, 4, 5, 6 you can get with a deck of 52 cards. Please help.<BR>\n" );
document.write( "NORMALLY WE COUNT AN ACE AS 1,JACK/QUEEN/KING AS TEN AND THE REST AS PER THE NUMBERS ON THEM.IS THIS THE PRACTICE OR ANY OTHER COUNT IS THERE?<BR>\n" );
document.write( "SURE..BUT FIRST CLARIFY PLEASE.YOU CAN MAIL THE SITE ACKNOWLEDGING THIS RESPONSE AND ALSO POST REVISED QUESTION IN THE SITE.<BR>\n" );
document.write( "AT THE OUTSET THERE ARE LIMITED POSSIBILITIES ONLY..FOR EXAMPLE WITH<BR>\n" );
document.write( "2 CARDS, SUM POSSIBLE IS 2 TO 20....SUCCESS CASES ARE THOSE TOTALING 2,11,20 ONLY<BR>\n" );
document.write( "3 CARDS.....SUM....3 TO 30 ...SUCCESS...3,12,21,30...ETC....\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
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