Bijections Galore

Ram has 2018 coins.

The \(1^\text{st}\) coin has a \(\frac{1}{2}\) chance of flipping heads, the \(2^\text{nd}\) coin has a \(\frac{1}{3}\) chance of flipping heads, the \(3^\text{rd}\) coin has a \(\frac{1}{5}\) chance of flipping heads, continuing such that the \(k^\text{th}\) coin has a \(\frac{1}{p(k)}\) chance of flipping heads, where \(p(k)\) is the \(k^\text{th}\) 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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