Suppose that 2 books are picked at random from a shelf containing 7 novels, 3 books of poems, and a dictionary. (a) Find the probability that the dictionary is selected. (b) Find the probability that 1 novel and 1 book of poems are selected.

(a) Probability that the dictionary is selected = 0.1818

(b) Probability that 1 novel and 1 book of poems are selected = 0.3818

Step-by-step explanation:

We are given that 2 books are picked at random from a shelf containing 7 novels, 3 books of poems, and a dictionary.

(a) Probability that the dictionary is selected is given by;

Number of ways of selecting a dictionary from total of 1 dictionary from the shelf = = 1

Now, since two books are picked from the shelf from which one is dictionary so another book will be from total 10 books (7 novels + 3 poems), so number of ways for doing this = = 10

Number of ways of selecting total 2 books from total of 11 books from the shelf = = 55

So, required probability = = = 0.1818

(b) Number of ways of selecting 1 novel from total of 7 novels from the shelf = = 7

Number of ways of selecting 1 book of poem from total of 3 books of poems from the shelf = = 3

Number of ways of selecting total 2 books from total of 11 books from the shelf = = 55

So, probability that 1 novel and 1 book of poems are selected =

                                       = = 21/55 = 0.3818

To find the answer, multiply the number of routes because it gives the number of permutations (choices) you can take. 
There are 3 routes between school and the library.
 There are 5 routes from the library to her home. 
 Therefore, there are 3 x 5 = 15 total routes