Final answer:
The probability of drawing a fiction book first and then a hardcover book second, when drawing without replacement, is 0.4242
Step-by-step explanation:
To determine the probability of drawing a fiction book first and then a hardcover book second, when drawing without replacement, we can use the concept of conditional probability. Let's denote the events as follows:
F: Drawing a fiction book
H: Drawing a hardcover book
The probability of drawing a fiction book first is 8 out of 12, since there are 8 fiction books out of a total of 12 books on the shelf. After drawing a fiction book, there are now 7 fiction books left out of a total of 11 books on the shelf. So, the probability of drawing a hardcover book second, given that a fiction book was drawn first, is 7 out of 11. Therefore, the probability of drawing a fiction book first and then a hardcover book second is (8/12) * (7/11) = 0.4242 (rounded to four decimal places).