Since the spot price of the put option is higher than the strike price, the option is out of the money. The payoff to the option buyer is:

P_T = max(0, X - S_T) = max(0, 65 - 78) = 0

A note on puts: A short put refers to the opening of an options trade by selling or writing a put option. The trader who buys the put option is long that option (holds the long position), and the trader who wrote that option is short (holds the short position).

For the long position (buyer), the option is in the money (ITM) if and only if the prevailing spot price at expiry is less than the strike price. In such circumstances, the buyer would be able to "cut" their loss by selling the underlying at the strike price, which would be considerably higher than the prevailing market price. Buyers of puts are bearish, i.e., they expect the underlying to lose value over time.

In this case, the spot price ($78) is greater than the strike price ($65), so the put option expires worthless, and the payoff is $0.