I toss two coins and look at the outcome.
I then tell you that at least one of the coins is showing up as "tails". What is the chance that the other one is showing "tails" as well?
(from techInterview.org)
(In reply to
re: Question On The Solution by Charlie)
In fact, a simulation follows:
OPEN "cointoss.txt" FOR OUTPUT AS #2
FOR trial = 1 TO 400
coin1$ = MID$("ht", INT(RND(1) * 2) + 1, 1)
coin2$ = MID$("ht", INT(RND(1) * 2) + 1, 1)
PRINT #2, coin1$; coin2$; " ";
which = INT(RND(1) * 2) + 1
SELECT CASE which
CASE 1: report$ = coin1$
CASE 2: report$ = coin2$
END SELECT
PRINT #2, CHR$(34); "At least one is a ";
IF report$ = "h" THEN PRINT #2, "heads"; : ELSE PRINT #2, "tails";
PRINT #2, "."; CHR$(34)
IF report$ = "t" THEN
tailRpt = tailRpt + 1
IF coin1$ = "t" AND coin2$ = "t" THEN bothTails = bothTails + 1
END IF
NEXT
PRINT tailRpt, bothTails, bothTails / tailRpt
CLOSE
where the result had 193 cases of the narrator reporting at least one tails, in which 97 cases were of both being tails, for an observed probability of .5025907. In each case the choice as to which to report was made randomly with equal probability; it was not always the first one or always the second one, and no preference was given to reporting either heads or tails.
tt "At least one is a tails."
hh "At least one is a heads."
ht "At least one is a tails."
th "At least one is a tails."
tt "At least one is a tails."
tt "At least one is a tails."
th "At least one is a heads."
th "At least one is a heads."
hh "At least one is a heads."
th "At least one is a tails."
tt "At least one is a tails."
tt "At least one is a tails."
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th "At least one is a heads."
th "At least one is a heads."
hh "At least one is a heads."
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th "At least one is a tails."
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Posted by Charlie
on 20071024 10:38:57 