Elizabeth brought a box of donuts to share. There are two-dozen (24) donuts in the box, all identical in size, shape, and color. Four are jelly-filled, 4 are lemon-filled, and 16 are custard-illed. You randomly select one donut, eat it, and select another donut. Find the probability of selecting a lemon-illed donut followed by a jelly-filled donut. \( \square \) (Type an integer or a simplified fraction.)

To find the probability of selecting a lemon-filled donut first and then a jelly-filled donut, we can use multiplication of probabilities. The probability of selecting a lemon-filled donut first: \[ P(\text{lemon}) = \frac{4}{24} = \frac{1}{6}. \] After selecting a lemon-filled donut, there are now 23 donuts left, with 4 jelly-filled donuts remaining. The probability of selecting a jelly-filled donut next: \[ P(\text{jelly | lemon}) = \frac{4}{23}. \] Now, multiply these probabilities together: \[ P(\text{lemon then jelly}) = P(\text{lemon}) \times P(\text{jelly | lemon}) = \frac{1}{6} \times \frac{4}{23} = \frac{4}{138} = \frac{2}{69}. \] So the probability of selecting a lemon-filled donut followed by a jelly-filled donut is \( \frac{2}{69} \).