Question

Determine whether the given event is independent or dependent. Then find the probability. There are 3 literature books, 4 geography books, and 3 science books on a shelf. If 3 books are chosen at random one after the other, what is the probability that a literature book, a geography book, and a science book are selected if replacement does not take place?

Answer 1

The given event is dependent. The probability can be found using the multiplication rule.

Step-by-step explanation:

To determine whether the given event is independent or dependent, we need to consider whether the probability of selecting one type of book is affected by the previous selections. Since replacement does not take place, the events are dependent. The probability can be found using the multiplication rule.

Step 1: Determine the probability of selecting a literature book: P(literature) = (number of literature books)/(total number of books) = 3/10

Step 2: Determine the probability of selecting a geography book after selecting a literature book: P(geography|literature) = (number of geography books)/(remaining number of books) = 4/9

Step 3: Determine the probability of selecting a science book after selecting a literature and geography book: P(science|literature and geography) = (number of science books)/(remaining number of books) = 3/8

Step 4: Multiply the probabilities of the three events: P(literature and geography and science) = P(literature) * P(geography|literature) * P(science|literature and geography) = (3/10) * (4/9) * (3/8) = 1/10

Therefore, the probability that a literature book, a geography book, and a science book are selected, without replacement, is 1/10.

Answer 2

This is an independent event because picking on book at random has nothing to do with picking the next book at random. The probability is 1/7