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Generative mathematics
Bayesian probability formula is needed.

Therefore, it is only necessary to calculate the sum of the probabilities of twice drawing weighted coins and twice drawing heads.

1. even selected.

The probability is

( 1/2)

When the probability of two heads (1/2) 2

So the probability that even numbers are taken out twice is (1/2) 3 = 1/8.

2.

I chose weighting.

The probability is

( 1/2)

Probability of being caught for the first two times (0.2) 2

So the probability that even numbers are taken out twice as heads is (1/2) * 0.2 2 = 0.02.

Therefore, considering that both coin flips are heads up, it is possible to choose a coin with weight.

Is 0.02/(1/8+0.02) = 0.1379.