OK, I'll suggest you consider a similar problem.

Suppose you have two bags. Bag 1 has 55 orange balls and 45 hwite balls. Bag 2 has 100 orange balls and zero hwite balls.

You pick a bag at random and remove n balls without replacement. How many balls do you need to remove before being 99% confident that you picked bag 2?

To get you started:

Let m be the number of balls removed.

On the one hand: Pr(Bag 2 | no hwite balls removed in m drawings)

.

On the other hand:

Pr(Bag 2 | no hwite balls removed in m drawings)

= Pr( Bag 2 and no hwite balls removed in m drawings)/Pr(no hwite balls removed in m drawings)

= 0.5/Pr(no hwite balls removed in m drawings).

But Pr(no hwite balls removed in m drawings) = Pr(no hwite balls removed in m drawings | bag 1) Pr(Bag 1) + Pr(no hwite balls removed in m drawings | bag 2) Pr(Bag 2) = (......) (0.5) + 0.5.

Therefore

......

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