What's the expected number of outcomes covered by 1 million rolls of a 10-million-sided die?

Question

What I mean is the expected number of distinct sides that will get rolled. It's less than 1 million, because very likely, some side will get rolled more than once.

Answer 1

dude if you can build it I will try it out for ya an give the results! reaper out......

Answer 2

There is only one outcome expected, and that is the one that you roll. In other words, if you roll your 10 million sided die 1 million times, you will get only one outcome.

If you roll that same die another million times, you will get another outcome.

The number of possible outcomes (with no duplications) is given by:

10,000,000! / [(10,000,000-1,000,000)] !

Where "!" is factorial. For instance, 5! is 1x2x3x4x5.

So, with factorials, and your enormous numbers, the number of possible outcomes, given unlimited million rolls is quite large indeed.

As you mention, it is very likely that a side will be rolled more than once, but not very likely on the second roll. The likelihood increases the more times you roll. For instance, the 100th roll will be more likely to duplicate one of the previous 99.

However, each roll still only gives 1/10,000,000 chance of any given number.

So, suffice to say, the combinations alone are mindboggling.

For instance, picking 6 numbers in a lottery. There are over 2.7 billion combinations with only 40 numbers, and none are duplicated.

Good luck & hope it helped.

Regards,

Mysstere

Answer 3

no of live cells in ur body no of outcomes