Question

Ivan is getting ready for a long road trip. He wants to pack a few books from his collection of 5 novels and 7 collected short stories books. He asks his friend to select a book without showing. From the remaining books, Ivan then himself picks a random book, which turns out to be a novel. The third book that he randomly selects from the remaining ones is also a novel. Find the probability that Ivan will have 3 novels to read during the road trip.

Answer 1

The probability that Ivan will have 3 novels to read during the road trip is 0.0455

Explanation:

Given;

number of novels = 5

number of short stories = 7

total number of books = 12

The probability that Ivan's friend pick's a novel = 5 / 12

The probability of Ivan's first pick to be a novel = 4 / 11

The probability of Ivan's second pick to be a novel = 3 /10

The probability that Ivan will have 3 novels to read during the road trip is given by;

= p(Ivan's friend pick) and P(Ivan's first pick) and P(Ivan's second pick);

`= (5)/(12)*(4)/(11)*(3)/(10)\\\\ = (1)/(22)\\\\ = 0.0455`

Therefore, the probability that Ivan will have 3 novels to read during the road trip is 0.0455