Question

A bookshelf contains 9 mysteries and 7 biographies books. A book is randomly selected and not replaced.

What is the probability that the first book is mystery and the second is the biography?

Answer 1

The answer is 7/30

Explanation:

According to counting rules, we use permutation when we want to choose successively and without replacement, as given in this problem

Rule of permutation: nPr = n! /(n-r)!

where: n:objects and r:sample

n of mysteries=9 ; r of mysteries=1 ; ⇒ 9P1

n of biographies=7 ; r of biographies=1 ; ⇒ 7P1

n of total books=9+7=15 ; r of total books=2 ; ⇒15P2

Probability=( 9P1 x 7P1 ) / 15P2 = 49/210 = 7/30

Hope this helps :)