document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=710366>Question 710366</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider a game where 2 coins are tossed. $2 is bet on every 2 tosses and we win $4 in both coins land on heads.\r<BR>\n" );
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document.write( "(a) What are the expected winnings?\r<BR>\n" );
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document.write( "(b) Is this a fair game? If not, what amount should we bet to make it fair? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #436977 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=436977\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Consider a game where 2 coins are tossed. $2 is bet on every 2 tosses and we win $4 in both coins land on heads.<BR>\n" );
document.write( "P(2 heads) = (1/2)^2 = 1/4<BR>\n" );
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document.write( "(a) What are the expected winnings?<BR>\n" );
document.write( "Random number vales::: -2......+2<BR>\n" );
document.write( "Probabilities:::::::: (3/4)....(1/4)<BR>\n" );
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document.write( "E(x) = -2(3/4) + 2(1/4 = [-6+2]/4 = -$1.00<BR>\n" );
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document.write( "(b) Is this a fair game? <BR>\n" );
document.write( "It is not a fair game because you can expect to lose $1.00 each time you play.<BR>\n" );
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document.write( "If not, what amount should we bet to make it fair?<BR>\n" );
document.write( "Let the cost to play be \"x\" and you win $4.00 for 2 heads:<BR>\n" );
document.write( "Random value:::: -x......4-x<BR>\n" );
document.write( "Probabilities::::(3/4)...(1/4)<BR>\n" );
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document.write( "Let E(x) = 0 to make the game fair.<BR>\n" );
document.write( "E(x) = (-3/4)x + (1/4)(4-x) = 0<BR>\n" );
document.write( "[-3x + 4-x]/4 = 0<BR>\n" );
document.write( "-3x+4-x] = 0<BR>\n" );
document.write( "x = 1 (You should pay $1 to play the game)<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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