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Question 1
Carlos buys a bax of doughnuts. The box contains 3 chocolate glazed, 5 Boston crème, and 7 powdered sugar doughnuts. He reaches into the box and randomly selects a doughnut, then reaches into the box again and selects another doughnut.
What is the probability that he randomly selects a Boston crème first and then a chocolate glazed doughnut? Round your answer to three decimal places.
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Step 1 ：First, we calculate the total number of doughnuts in the box. The box contains 3 chocolate glazed, 5 Boston crème, and 7 powdered sugar doughnuts. So, the total number of doughnuts is \(3 + 5 + 7 = 15\).

Step 2 ：Next, we calculate the probability of Carlos selecting a Boston crème doughnut first. The number of Boston crème doughnuts is 5. So, the probability is \(\frac{5}{15} = 0.333\).

Step 3 ：After Carlos selects a Boston crème doughnut, the total number of doughnuts in the box decreases by one, becoming 14. We then calculate the probability of him selecting a chocolate glazed doughnut. The number of chocolate glazed doughnuts is 3. So, the probability is \(\frac{3}{14} = 0.214\).

Step 4 ：The final probability is the product of the two probabilities calculated above. So, the final probability is \(0.333 \times 0.214 = 0.071\).

Step 5 ：Final Answer: The probability that Carlos randomly selects a Boston crème first and then a chocolate glazed doughnut is \(\boxed{0.071}\).