Question

The top shelf of a bookcase holds 6 fiction and 4 nonfiction books. On the bottom shelf are 3 fiction and 5 nonfiction books. Choosing which 2 books describes a pair of dependent events?
A. one of the nonfiction books on the bottom shelf, and a second nonfiction book from the bottom shelf
B. one of the fiction books on the top shelf, and then one of the nonfiction books on the top shelf
C. one of the fiction books on the top shelf, and then one of the nonfiction books on the bottom shelf
D. one of the fiction books on the top shelf, and then a second fiction book from the bottom shelf

Answer 1

When one event's occurrence or non-occurrence doesn't affect the occurrence or non-occurrence of another event, then such events are called independent events. The correct option is B.

Which pair of events are called independent events?

When one event's occurrence or non-occurrence doesn't affect the occurrence or non-occurrence of another event, then such events are called independent events.

Symbolically, we have:

Two events A and B are said to be independent if we have:

$P(A \cap B) = P(A)P(B)$

Comparing it with the chain rule will give

$P(A|B) = P(A)\\P(B|A) = P(B)$

Thus, showing that whether one occurred or not, the other one doesn't care about it (independence).

The top shelf of a bookcase holds 6 fiction and 4 nonfiction books. On the bottom shelves, there are 3 fiction and 5 nonfiction books.

When Choosing 2 books that describe a pair of dependent events, one of the fiction books should be chosen from the top shelf, and another one should be a nonfiction book from the top shelf itself.

Hence, the correct option is B.

Learn more about probability here:

brainly.com/question/1210781

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