18 good fruits, 12 bad fruits are all in a bag. Total fruits in a bag = 30. Prob. that both are good.

The probability of drawing a good fruit on the first draw is the number of good fruits divided by the total number of fruits.

$$P(\text{1st good}) = \frac{\text{Number of good fruits}}{\text{Total number of fruits}} = \frac{18}{30}$$

After drawing one good fruit, there are now 17 good fruits left and a total of 29 fruits remaining in the bag.

$$P(\text{2nd good | 1st good}) = \frac{\text{Number of remaining good fruits}}{\text{Total remaining fruits}} = \frac{17}{29}$$

To find the probability that both events occur, multiply the probabilities from Step 1 and Step 2.

$$P(\text{both good}) = P(\text{1st good}) \times P(\text{2nd good | 1st good})$$ $$P(\text{both good}) = \frac{18}{30} \times \frac{17}{29}$$ $$P(\text{both good}) = \frac{3}{5} \times \frac{17}{29}$$ $$P(\text{both good}) = \frac{3 \times 17}{5 \times 29}$$ $$P(\text{both good}) = \frac{51}{145}$$

The probability that both fruits are good is $\frac{51}{145}$.