Question

A bookcase contains 3 statistics books and 5 biology books. If 2 books are chosen at random, the chance that both are statistics books is

a) 0.12
b) 12%
c) 8.33%
d) 833%

Answer 1

The chance that both books selected are statistics books is computed using combinations. It is found to be approximately 10.71%, with the closest answer choice given as 12%.

Step-by-step explanation:

The student asked what the chance is that both books chosen at random from a bookcase containing 3 statistics books and 5 biology books will be statistics books.

To find this probability, we use the formula for combinations because the order of selection does not matter:

P(both statistics books) = (number of ways to choose 2 statistics books) / (number of ways to choose 2 books from all books).

Number of ways to choose 2 statistics books = 3C2 = 3 ways (since there are 3 statistics books).

Number of ways to choose 2 books from all books = 8C2 = 28 ways (since there are 3 statistics + 5 biology = 8 total books).

So the probability is 3/28, which can be approximated as 0.1071 or 10.71%. The option closest to this value is b) 12%.