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# If you flip a fair coin 19 times, what is the probability that you will end up with an even number of heads?

$\begin{array}{1 1} \frac{1}{2} \\ \frac{1}{3} \\ \frac{8}{18} \\ \frac{8}{19} \end{array}$

If we take the first 18 coil flips, the total number of heads will either be even or odd. If it's even, the 19th flip will keep the total even with a probability of 1/2. If odd, it will convert to even with same probability. Hence, the answer is 1/2.