Final answer:
To find the probability of picking 2 mathematics books out of 5 from a shelf with 7 mathematics, 3 physics, and 2 chemistry books, we calculate the combinations of selecting books and divide the favorable outcomes by the total outcomes. The probability is approximately 26.52%.
Step-by-step explanation:
The student asked about the probability that 2 mathematics books are selected when 5 books are picked at random from a shelf containing 7 mathematics, 3 physics, and 2 chemistry books. To solve this, we can use combinations to find the different ways to select the books.
The total number of ways to pick 5 books from 12 is calculated by the combination formula C(12,5). The number of ways to pick exactly 2 mathematics books out of 7 is C(7,2) and the number of ways to pick the remaining 3 books from the 5 non-mathematics books is C(5,3). The probability is then calculated by dividing the number of ways to pick 2 mathematics and 3 non-mathematics books by the total number of ways to pick any 5 books.
Total books: 12 (7 math, 3 physics, 2 chemistry)
Total ways to pick 5 books: C(12,5) = 792
Ways to pick 2 mathematics books: C(7,2) = 21
Ways to pick 3 non-mathematics books: C(5,3) = 10
Probability of picking 2 mathematics books: (C(7,2) * C(5,3)) / C(12,5)
This gives us (21 * 10) / 792 which simplifies to 210 / 792. After simplifying, we have the probability which is approximately 0.2651515 or 26.52%.