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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[1]=x[2]; x[2]=x[3]; x[3]=random(2); y[1]=y[2]; y[2]=y[3]; y[3]=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
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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!

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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[1]=x[2]; x[2]=x[3]; x[3]=random(2); y[1]=y[2]; y[2]=y[3]; y[3]=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
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