Q53

Suppose an unbiased coin is tossed $6$ times. Each coin toss is independent of all previous coin tosses. Let $E_{1}$ be the event that among the second, fourth, and sixth coin tosses, there are at least two heads. Let $E_{2}$ be the event that among the first, second, third, and fifth coin tosses, there are equal number of heads and tails. The conditional probability $\mathrm{P}\left(E_{1} \mid E_{2}\right)$ is equal to $\_\_\_\_\_\_\_$. (rounded off to one decimal place)