Bijections Galore

Probability Level 1

Ram has 2018 coins.

The 1st1^\text{st} coin has a 12\frac{1}{2} chance of flipping heads, the 2nd2^\text{nd} coin has a 13\frac{1}{3} chance of flipping heads, the 3rd3^\text{rd} coin has a 15\frac{1}{5} chance of flipping heads, continuing such that the kthk^\text{th} coin has a 1p(k)\frac{1}{p(k)} chance of flipping heads, where p(k)p(k) is the kthk^\text{th} prime number.

Ram flips each of his coins once.

What is the probability that Ram flips an even number of heads?

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