Elizabeth brought a box of donuts to share. There are two-dozen (24) donuts in the box, all identical in size, shape, and color. Two are jelly-filled, 9 are lemon-filled, and 13 are custard-filled. You randomly select one donut, eat it, and select another donut. Find the probability of selecting a custard-filled donut followed by a lemon-filled donut.
Answer
The probability of selecting a custard-filled donut followed by a lemon-filled donut is approximately \(\boxed{0.212}\).
Step 1 ：The problem is asking for the probability of two independent events: first selecting a custard-filled donut, and then selecting a lemon-filled donut. The probability of two independent events occurring is the product of their individual probabilities.
Step 2 ：First, we need to calculate the probability of selecting a custard-filled donut. There are 13 custard-filled donuts out of a total of 24. So, the probability is \(\frac{13}{24} = 0.5416666666666666\).
Step 3 ：Then, we need to calculate the probability of selecting a lemon-filled donut after one donut has already been taken. There are 9 lemon-filled donuts out of a total of 23 remaining donuts. So, the probability is \(\frac{9}{23} = 0.391304347826087\).
Step 4 ：Finally, we multiply these two probabilities together to get the final answer. \(0.5416666666666666 \times 0.391304347826087 = 0.21195652173913043\).
Step 5 ：The probability of selecting a custard-filled donut followed by a lemon-filled donut is approximately \(\boxed{0.212}\).
