Q22

A box contains $5$ coins: $4$ regular coins and $1$ fake coin. When a regular coin is tossed, the probability $P($ head $)=0.5$ and for a fake coin, $P($ head $)=1$. You pick a coin at random and toss it twice, and get two heads. The probability that the coin you have chosen is the fake coin is __________. (rounded off to two decimal places)