Binomial Option Pricing Model $-$ IV

A stock is priced at $$50.$ Over each of the next two $3-$month periods, it is expected

to go up by $6\%$ or down by $5\%.$ The risk$-$free interest rate is $5\%.$

What is the risk$-$neutral probability of the stock price going up$?($at least $4$ decimal

places$)$

What is the price of an American put option with a strike of $$51?($at least $2$

decimal places$)$

Note: you should find that the option will be exercised somewhere.