passes 90% of the time depends on you, do you have some other reasom to
suspect the coin? Otherwise you may suspect it and possibly do somemore tests.
If it fails a 99% test you may have more reason to suspect the coin.
Another (slightly different) explanation . . .
How many times does one have to roll a die in order
to have face 5 showing up with a 90% certainty?
We know that for one roll: .
Consider consecutive rolls without a 5.
. . This probability is: .
And we want this probability to be less than 10%.
. . Hence, we have: .
Take logs: .
. . Divide by which is negative: .
Therefore, one must roll a die at least 13 times.