If dice are tossed 10,000 times, and all 10,000 outcomes are multiplied, what is probability that the first digit (that is most significant digit) of the product is 5?
2007-11-26 03:27:54 · 2 answers · asked by Alexander 6 in Science & Mathematics ➔ Mathematics
If we consider the distribution f(x), where x is the product and f(x) is the number of different ways the dice can be thrown to result in this product, and that the shape of this distribution f(x) is probably scale invariant (i.e., looks the same for 100,000, 1,000,000 throws, etc), then Bedford's Law probably holds, and therefore the odds of the most significant figure being 5 would be 7.918%.
Otherwise, this is just a miserable problem, and I need a lot more time to get a more precise answer. Anyone else can help?
2007-11-26 07:48:57 · answer #1 · answered by Scythian1950 7 · 3⤊ 0⤋
Let see, if we multiply it all out, the answers should center around 1.663 x 10^4672 and then we look at the log analysis of the statistical distribution. The answer becomes quite clear:
Approximately one out of nine or 11%
2007-11-26 14:22:21 · answer #2 · answered by Frst Grade Rocks! Ω 7 · 1⤊ 1⤋