Chance of a word repeating THREE times in a BIP39 Mnemonic passphrase? And what about 2 words repeating 2 times each?
The probability of 11.7% is being calculated using the birthday paradox formula.

"The paradox of birthdays is a mathematical problem put forward by Von Mises, who looks for the value N in the problem: In a group of N people there is 50% chance that at least 2 people in the group share the same birthday (day + month). The answer is N = 23, which is quite counterintuitive, hence the paradox."

So for the calculations:
-Repetition (Twice): 2 (number of people sharing the same birthday)
-Number of words: 24 (number of people in a group)
-Number of all BIP39 words: 2048 (number of days in a year)

The result is 0.119 (11.9%). 
But for THREE repetitions it's getting really low: 0.00043 (0,043%). 

Answering the question about two words both repeated twice, would require reworking the formula. I used an online calculator to provide the values.