A binary option pays off $$165$ if a stock price is greater than $$65$ in three months. The current stock price is $$50$ and its volatility is $40\%.$ The risk$-$free rate is $4\%$ and the expected return on the stock is $10\%.$ Note that some of the subsequent values were assumed and not calculated.

The risk$-$neutral probability of the payoffs $($d$2)$ is$...$