Binomial Option Pricing in One Period: interest rate is $20\%$ for one period, simple

compounding. Stock price today is $60,$ after one period, it either goes up to $90$ or down to $54.$

And we have a European put with a strike price of $72.(10)$

a$.$ What are the risk$-$neutral probabilities of stock price goes up and down in next

period? $(3)$

b$.$ What is the price of the European put today? $(3)$

c$.$ Would the value of the corresponding American put be the same?