Question

I am having trouble with all three parts.

A shelf contains 3 novels, 2 books of poetry, and 1 dictionary. We select 2 books at random in turn without replacement. Define events A and N by: A = “the dictionary is selected”, N = “at least one novel is selected”. Show your work to find each of the following:

(a) P(A' )

(b) P(N)

(c) P(A ∩ N).

Answer 1

(a)
Novels = 3

Poetry = 2

Dictionary = 1

Total = 6

Books selected = 2

A = Dictionary is selected

N = At least 1 Novel is selected.

Case1:

Selection 1: Dictionary is selected.

P(Selection 1) = 1/6

Selection 2: Other than Dictionary isselection.

P(Selection 2)=1 since there is only 1 Dictionary.

So,

P(Case 1) = 1/6

Case 2:
Selection 1: Dictionary is not selected.

P(Selection 1) = 5/6.

Selection 2: Dictionary is selected.

P(Selection 2) = 1/5, because number of books = 5 after 1 is selected in Selection 1.

So,

P(Case 2) = 5/6 X 1/5 = 1/6

So,

P(A) =1/6 + 1/6 = 1/3

So,

P(A') = 1 - 1/3 = 2/3

(b)

Selection 1:No novel selected.

So,

P(Selection 1)= 5/6

Selection 2: No novel selected

So,

P(Selection 2) =4/5

So,

P(NoNovel selected) = 5/6 X 4/5 = 4/6 = 2/3

So,

P(N) = 1 - 2/ 3 = 1/3

(c)

P(AN) = P(Dictionary is selected AND at least one novel is selected) = P(Dictionary AND 1 Novel selected) = 1/3 X 1/3 =1/9