Question

On a bookshelf there are seven fiction books and six nonfiction books Paul randomly selects one puts it back and then randomly selects another what is the probability that both selections were fiction books

Answer 1

Pick 1: 7 fiction out of 13 total books = 7/13
Pick 2: 7 fiction out of 13 total books = 7/13

Pick 1 AND Pick 2
  7/13    x      7/13  = 49/169

Answer 2

Answer: $\dfrac{49}{169}$

Step-by-step explanation:

Given: Number of fiction books = 7

Number of nonfiction books = 6

Probability of fiction books =$\dfrac{\text{Number of fiction book}}{\text{Total book}}=\dfrac{7}{13}$

Since , Paul randomly selects one puts it back.

Then the number of books remains same and events will be independent.

Now, if he randomly selects another then the probability that both selections were fiction books will be:

$\dfrac{7}{13}\times\dfrac{7}{13}=\dfrac{49}{169}$

Hence, the  required probability = $\dfrac{49}{169}$