a) I have a pair of fair nsided dice. The probability when both are rolled that their results differ by two is the same as that the sum will be 5 or less. Find n.
b) I have two dice, one with n sides and the other with m sides. When they are rolled the probability they are equal is the same as that they sum to 13 or higher. Find n and m.
c) I have a trio of nsided dice. When I roll them all the probability that the dice all show different numbers is greater than when they sum 15 or less but less than when they sum 16 or less. Find n.
Note: "x sided dice" are numbered with consecutive integers from 1 to x.
(In reply to
re: Part c) clarified. by Charlie)
Part c works if "15 or less" is replaced by "less than 15", and similarly for 16, with the answer being n=8:
3 0.2222222222 1.0000000000 1.0000000000
4 0.3750000000 1.0000000000 1.0000000000
5 0.4800000000 0.9920000000 1.0000000000
6 0.5555555556 0.9074074074 0.9537037037
7 0.6122448980 0.7551020408 0.8367346939
8 0.6562500000 0.5937500000 0.6835937500
9 0.6913580247 0.4581618656 0.5418381344
10 0.7200000000 0.3520000000 0.4250000000
11 0.7438016529 0.2712246431 0.3328324568
12 0.7638888889 0.2106481481 0.2615740741
FOR n = 3 TO 12
succDiff = 0: t15Ct = 0: t15suc = 0: t16Ct = 0: t16suc = 0
FOR a = 1 TO n
FOR b = 1 TO n
FOR c = 1 TO n
IF a <> b AND a <> c AND b <> c THEN
success = 1
ELSE
success = 0
END IF
succDiff = succDiff + success
t = a + b + c
IF t < 15 THEN
t15Ct = t15Ct + 1
t15suc = t15suc + success
END IF
IF t < 16 THEN
t16Ct = t16Ct + 1
t16suc = t16suc + success
END IF
NEXT
NEXT
NEXT
ways = n * n * n
PRINT n,
PRINT USING "##.##########"; succDiff / ways; t15Ct / ways; t16Ct / ways
NEXT
Edited on December 1, 2006, 3:04 pm

Posted by Charlie
on 20061201 15:03:13 