BTGmoderatorDC wrote: ↑Tue Mar 16, 2021 6:49 pm
Mathematics, physics, and chemistry books are stored on a library shelf that can accommodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many mathematics books as physics books and the number of physics books is 4 greater than that of the chemistry books. Ricardo selects 1 book at random from the shelf, reads it in the library, and then returns it to the shelf. Then he again chooses 1 book at random from the shelf and checks it out in order to read at home. What is the probability Ricardo reads 1 book on mathematics and 1 on chemistry?
A) 3%
B) 6%
C) 12%
D) 20%
E) 24%
OA
C
Solution:
Since 20% of the shelf is empty, 80% is full and thus, there are 25 x 0.8 = 20 books on the shelf.
Let c denote the number of chemistry books. Then, there are c + 4 physics books and 2(c + 4) = 2c + 8 mathematics books. Since the sum of the books on the three subjects is 20, we have:
c + (c + 4) + (2c + 8) = 20
4c + 12 = 20
4c = 8
c = 2
Thus, there are 2 chemistry books, c + 4 = 6 physics books and 2c + 8 = 12 mathematics books.
The probability that Richardo reads a mathematics books in the library and checks out a chemistry book is 12/20 x 2/20 = 24/400 = 6/100. The probability that he reads a chemistry book in the library and checks out a mathematics book is also 2/20 x 12/20 = 6/100. Thus, the probability that one mathematics and one chemistry book is read is 6/100 + 6/100 = 12/100 = 12%.
Answer: C
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