[LambSlave]

Odds of rolling (at least) one five in n rolls (assuming independence/equal likelihood of rolls) would be => 1 - (5/6)^n. So for six rolls you get 1 - 0.3348 = ~67% chance.

[Teacher317]

You're right, he only wants the number of expected connected calls out of 1000... the odds per caller do not change, so once we have the odds, we just multiply by 1000 to get the expected number of live contacts.

And since the calls stop once he gets a single "five" (a live contact), the odds of subsequent rolls are irrelevant (because they won't waste time calling again).

So the odds of getting at least one "five" in 6 rolls is the 66.52 percent chance LambSlave gave...

Multiply that by 1000 target clients, and it gives you 665.2 likely live phone contacts if you stop at 6 tries, and you have a 16 percent chance of a live contact per attempted call.