Mathematics, physics, and chemistry books are stored on a library shelf that can accommodate 25 ...
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?
Answer/Solution
12percent
Steps/Work
Shelf can accomodate 25 books but 20% of it is empty so there are in all 20 books.
If no of Chem books = x, number of Physics book = x+4, number of Math books = 2(x+4)
x + x+4 + 2(x+4) = 4x + 12 = 20
x = 2
Chem books = 2, Phy books = 6, Math books = 12
Probability of picking a Math book = 12/20
Probability of picking a Chem book = 2/20
Total Probability = Pick Math first and then Chem + Pick Chem first and then Math
= (12/20) * (2/20) + (2/20) * (12/20) = 12/100 = 12%
If no of Chem books = x, number of Physics book = x+4, number of Math books = 2(x+4)
x + x+4 + 2(x+4) = 4x + 12 = 20
x = 2
Chem books = 2, Phy books = 6, Math books = 12
Probability of picking a Math book = 12/20
Probability of picking a Chem book = 2/20
Total Probability = Pick Math first and then Chem + Pick Chem first and then Math
= (12/20) * (2/20) + (2/20) * (12/20) = 12/100 = 12%