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Chapter 5: Q 2.1. (page 317)

Shuffle a standard deck of cards, and turn over the top card. Put it back in the deck, shuffle again, and turn over the top card. Define events A: first card is a heart, and B: second card is a heart.

Short Answer

Expert verified

Yes, events are independent.

Step by step solution

01

Step 1. Given Information

There are two events A and B .

A: First card is a heart.

B : Second card is a heart.

02

Step 2. Concept Used

If the occurrence of one event has no bearing on the likelihood of the other, the two events are said to be independent. In other words, if P(A|B)=P(A) and P(B|A)=P(B), events A and B are independent (B).

03

Step 3. Explanation

The first card is returned to the deck after which the deck is reshuffled before picking the second card. It signifies that the selected first card provides no information regarding the second chosen card. As a result, the two events are distinct.

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