I threw a coin n times, and never got three tails in a row. I calculated the odds of this event, and found out they were just about even; 50%-50%. How many times did I throw the coin?

A second question: what were the chances of having not gotten three heads in a row either?

(In reply to Exhaustion--1st and 2nd questions by Charlie)

The program which produced the exhaustive list of H-T sequences and counted results is:

DECLARE SUB toss ()
OPEN "ctoss.txt" FOR OUTPUT AS #2
DIM SHARED s$, Tctr, Hctr, Bctr, Nctr
  toss
PRINT #2, : PRINT #2, "TTT"; Tctr; "; HHH"; Hctr; "; both"; Bctr; "; neither"; Nctr
CLOSE
END

SUB toss
 IF LEN(s$) = 10 THEN
   PRINT #2, s$; " ";
   ix1 = INSTR(s$, "TTT")
   ix2 = INSTR(s$, "HHH")
   IF ix1 THEN PRINT #2, "TTT "; : Tctr = Tctr + 1
   IF ix2 THEN PRINT #2, "HHH "; : Hctr = Hctr + 1
   IF ix1 > 0 AND ix2 > 0 THEN Bctr = Bctr + 1
   IF ix1 = 0 AND ix2 = 0 THEN Nctr = Nctr + 1
   PRINT #2,
 ELSE
     s$ = s$ + "H"
     toss
     s$ = LEFT$(s$, LEN(s$) - 1) + "T"
     toss
     s$ = LEFT$(s$, LEN(s$) - 1)
 END IF
END SUB

 

Posted by Charlie on 2004-06-13 11:53:37