Not sure if the info given is enough to figure out the exact probability here — can someone help?

Question

Each of the 45 books on a shelf is written either in English or in Spanish, and each of the books is either a hardcover book or a paperback. If a book is to be selected at random from the books on the shelf, is the probability less than 1/2 that the book selected will be a paperback written in Spanish?

1. Of the books on the shelf, 30 are paperbacks.
2. Of the books on the shelf, 15 are written in Spanish

1. Of the books on the shelf, 30 are paperbacks. 
2. Of the books on the shelf, 15 are written in Spanish

Mohit C · Accepted Answer

This question is about checking whether the probability of picking a paperback written in Spanish is less than 1/2 . Total books = 45. We need to know how many of them are both paperback and in Spanish.
Statement 1 tells us that 30 books are paperbacks. But it doesn&rsquo;t say how many are written in Spanish. It&rsquo;s possible that 25 of them are in Spanish  in that case, the probability would be more than 1/2. But if only 5 of the paperbacks are in Spanish, then the probability would be far less than &frac12;. So this statement alone is not sufficient.
Statement 2 tells us that 15 books are written in Spanish. That means even if all 15 Spanish books are paperbacks, the probability of picking one is at most 15/45, or 1/3, which is definitely less than 1/2. So this statement alone is sufficient. Answer is B , only Statement 2 is sufficient.

Divakshi Arora · Answer

This one comes down to the overlap between Spanish books and paperbacks.

Statement 1 says there are 30 paperbacks, but gives no info about how many of them are in Spanish. The number of Spanish paperbacks could vary, so this is not sufficient.
Statement 2 tells us 15 books are in Spanish. Even if all of them are paperbacks, that&rsquo;s 15 out of 45, which is exactly one-third.
One-third is less than one-half, so the probability is definitely less than one-half. Statement 2 alone is sufficient.

Only Statement 2 gives a definite answer. Correct answer is B.