Probability of stock price in a month calc

Find implied volatility and expected rate of return (using CAPM for example). Convert rate of return to monthly, compute expected price in a month, and then use implied volatility to build a distribution (normal for example) around that price. Then use normal tables to compute Probability(Price > X) at that point. Sure this is over-simplified but close enough. If you want more technical answer then use google.

if you're extracting implied vol from the black-scholes model, then that implied vol is the STDEV of log returns of the stock, not the STDEV of the stock price itself. if the option prices from which you extract implied vol are calculated using a different model (which might not assume log-normal stock prices), then what I said would not apply because implied vol could be the STDEV of something different

If you're looking across different strikes, the probability of exercise (i.e. the chance it reaches/exceeds a certain price) can be determined by the N(d2) compenent in Black-Scholes.

Price a 1m 1-touch option, I'm sure you can do this in Bloomberg.

And if you are really in a hurry and don't have the time to calculate the probability just use the z-tables. Otherwise just use probability as mentioned by Dr Joe.

Just take a call option with Strike = X, maturity = 1m, and the implied vol you have And compute its delta with a pricer / Black scholes formulas. The delta is roughly the probability to finish in the money(it is exactly the case if interest rates are 0), which is precisely what you look for.