I calculated that from a scale of 0 and 1, we have a 0.33 chance of going in in 0 days.
The probability of going in within 1 day is equal to the probability of choosing the second door (0.33) multiplied to the probability of choosing the first door the second time (0.33). 0.33 * 0.33 is equal to 0.1089, so we have a 10% chance of getting in with 1 days.
To get in in 2 days, we would have to choose the second door, and then the first door. Again, this is another 10%
At this point I thought that we have a 53% chance of getting in within two days (33% + 10% + 10%), and 47% of getting in with more than 2 days.
The probability of getting in within 3 days is 0.33 * 0.33 * 0.33, which is around 3%. Considering that the probability of getting in within 4 days would be 1% (0.33 * 0.33 * 0.33 * 0.33), I somehow imagined that of the remaining 47% of chances of getting in within more than two days, the 75% was represented by the probability of getting in within 3 days. The 75% of 47% is 35.2%, which is slightly higher than the chance of getting in within 0 days. The answer is 3.
Given that I lack math background, I wonder if my way of solving this problem is correct (hopefully someone can follow my reasoning).