In binomial option valuation, we need to know the expected return on the stock (that is, we need the probability of the stock increasing or decreasing). True or False?

Instead of buying a protective put, we can sell a percent of our portfolio equivalent to the positive delta of a put option on the portfolio (though we have to continuously match the delta over time). True or False?

A call option with a $55 strike price and a year to expiration has a $2.50 premium. The stock price today is $50, and the risk-free rate is 5%. What is the put premium (same strike and expiration) today?