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### AJB

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 14 Coin Flip

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 Coin Flip You should really be more careful how you ask the question. You're asking for an exact answer to a question about a future event. That is impossible (mathematically/logically). Instead you mean to be asking: "Is Monday's number more likely to be higher, lower, or equal to Tuesday's number?" Also, I get 9 and 7 (not 10 and 8) using a simple Monte Carlo simulation implemented in PARI/GP with the following lines. (Note in PARI/GP each command prompt starts with "?" and each echoed result starts with "%[ans #]": ``````? nx=0; ny=0; totalx=0; totaly=0; ? x=[2,2,2]; ? y=[2,2,2]; ? xcounter=0; ycounter=0; ? for(a=1,1000000,x=x; x=x; x=random(2); y=y; y=y; y=random(2); if(x==[0,1,0],totalx=totalx+nx; xcounter=xcounter+1; nx=0; x=[2,2,2], nx=nx+1); if(y==[0,1,1],totaly=totaly+ny; ycounter=ycounter+1; ny=0; y=[2,2,2], ny=ny+1);) ? totalx/xcounter*1. %50 = 8.9860094468688522953095197675231428315 ? totaly/ycounter*1. %51 = 6.9901880098759118838541625050937652314 `````` context Coin Flip Oh no, I think I should have initialized nx=1 and ny=1, which would have given me 10 and 8, so I think you were correct! context Coin Flip Corrected code :) ``````? nx=1; ny=1; totalx=0; totaly=0; ? x=[2,2,2]; ? y=[2,2,2]; ? xcounter=0; ycounter=0; ? for(a=1,1000000,x=x; x=x; x=random(2); y=y; y=y; y=random(2); if(x==[0,1,0],totalx=totalx+nx; xcounter=xcounter+1; nx=1; x=[2,2,2], nx=nx+1); if(y==[0,1,1],totaly=totaly+ny; ycounter=ycounter+1; ny=1; y=[2,2,2], ny=ny+1);) ? totalx/xcounter*1. %9 = 9.9747538727020637786400406970364976609 ? totaly/ycounter*1. %10 = 8.0048669591111395728602990618295923922 `````` context