The current price of a non-dividend-paying stock is $38.01 and you expect the stock price to either go up by a factor of 1.372 or down by a factor of 0.729 over the next 0.4 years.

A European put option on the stock has a strike price of $38 and expires in 0.4 years. The risk-free rate is 5% (annual, continuously compounded).

What is the option payoff if the stock price goes down?

What is the risk-neutral probability of an up movement?

What is the value of the option?