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
Exhaustion1st and 2nd questions by Charlie)
The program which produced the exhaustive list of HT 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 20040613 11:53:37 