document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1125025>Question 1125025</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Every day, Quinn either gains two pounds (with probability 1/2) or loses one pound (with probability 1/2). Each day these probabilities are independent of whether she lost or gained weight any other day. \r<BR>\n" );
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document.write( "At the end of four days, what's the probability that Quinn will weigh one pound less than she did before? <BR>\n" );
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document.write( "At the end of four days, what's the probability that Quinn will weigh one pound more than she did before? <BR>\n" );
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document.write( "Enter your answers as whole numbers or fractions in lowest terms. </SPAN>\n" );
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document.write( "There are five possible changes in her weight over the four days:<BR>\n" );
document.write( "(1) gain all four days: 4(+2) = +8<BR>\n" );
document.write( "(2) gain 3 of 4 days: 3(+2)+1(-1) = +5<BR>\n" );
document.write( "(3) gain 2 of 4 days: 2(+2)+2(-1) = +2<BR>\n" );
document.write( "(4) gain 1 of 4 days: 1(+2)+3(-1) = -1<BR>\n" );
document.write( "(5) gain 0 of 4 days: 4(-1) = -4<br><BR>\n" );
document.write( "From this, we can see that the answer to the second question is 0 -- there is no possibility that her change in weight over four days is equal to +1.<br><BR>\n" );
document.write( "We also see that to lose one pound over the 4 days, she needs to gain 1 day and lose 3 days.  There are 4 ways she can do that -- do the weight gain on any one of the 4 days.<br><BR>\n" );
document.write( "There are 2 ways her weight can go each day; so over 4 days the number of different sequences of weight gains or losses is 2*2*2*2 = 2^4 = 16.<br><BR>\n" );
document.write( "So the probability of losing 1 pound over the 4 days is 4/16 = 1/4. </SPAN>\n" );
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