18%
For it to be raining all weekend, we need the probability that it will rain on Sunday, given that it is raining on Saturday.
To get the probability of one thing, given that we know the probability of the other thing, we need to multiply their probabilities together.
The probability that it will rain on Saturday is 30%
The probability that it will rain on Sunday is 60%
0.3 * 0.6 = 0.18
Therefore 18% chance that it will rain on both days.