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Mathematical probability problem (grade one) is extremely difficult to solve.
This is a conditional probability problem. Because it's complicated, I used the arrangement method.

First find the probability of event B, then find the probability of event A and event B * * *, and divide them.

The 100 faces are 50 groups, and each group has two faces. 100 faces are different from each other-this is the idea of arrangement.

For P(B), it is calculated in two cases, one is that the double-faced currency is in the top five, and the other is not in the top five.

Where: firstly, set the position of the double-faced coin, which is C (5,1); Which side the double-sided coin shows is C (21); For the remaining four positions, you need to select four from the remaining 49 normal coins and arrange them all; The back 45 needs to be completely arranged, but there are two kinds of surfaces, namely A (45,45) * 2 45.

Not among them: the first five coins need to be selected from C(49, that is, C (49,5), and then all of them are arranged, A (5 5,5); The remaining 45 coins are all arranged, and each coin has two sides, namely A (45,45) * 245.

For P(AB), that is, AB occurs at the same time, the first five still need to be selected from 49 and all of them are arranged, and the sixth indicates which plane has two kinds, namely C (49,5 5) * A (5 5,5) * C (2,1); The remaining 44 coins are all arranged, and each coin has two sides, namely A (44,44) * 244.

Simplified to 1/55.

If you do not understand, please ask again!