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heads and tails with n unfair coins

Source: 11th QEDMO p2 Juniors (6-8. 12. 2012) https://artofproblemsolving.com/community/c1512515_qedmo_200507

May 16, 2021
combinatoricsprobability

Problem Statement

NN unfair coins (with heads and tails on the sides) are thrown, with the kthk^{th} coin has got a chance of 12k+1\frac{1}{2k + 1} to land on tails.How high is the probability that an odd number of coins will show tails?
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