For a stock, you are given:

1. The current stock price is 90

2. The stock pays dividends continuously at a rate proportional to its price. The dividend yield is 2%

3. The stocks volatility is 20%

4. You use a three-period forward binomial tree to model the movement of the stock price. The length of each period is 3 months

You are also given that the continuously compounded risk-free rate is 10%

Consider a 9-month 90-strike American put on the stock, calculate the risk-neutral probability that option will be exercised before maturity.