Consider a simple one$-$period binomial framework, where you want to price a one$-$year European put with strike $$45$ on Stock X$.$ This stock does not pay dividends, is currently priced at $$50$ per share, and may either increase in value by $10\%$ or decrease in value by $10\%($simple$).$ Elsewhere in the economy, you observe a Stock Y $($that also does not pay dividends$)$ priced at $$100$ per share. Both a one$-$year call and one$-$year put on this Stock Y at a strike of $$101$ are priced at $$3.$ Based on this information what is the price of the put on Stock X$?$