Problem

Question Using a standard 52-card deck, Michelle will draw 6 cards with replacement. If Event $A=$ drawing all hearts and Event $B=$ drawing no face cards, which of the following best describes events $A$ and $B$ ? Select the correct answer below: independent dependent mutually exclusive complement FEEDBACK MORE INSTRUCTION SUBMIT Content attribution

Solution

Step 1 :Understand the definitions of the terms given in the options: independent, dependent, mutually exclusive, and complement.

Step 2 :Two events are independent if the occurrence of one does not affect the probability of the occurrence of the other.

Step 3 :Two events are dependent if the occurrence of one affects the probability of the occurrence of the other.

Step 4 :Two events are mutually exclusive if they cannot both occur at the same time.

Step 5 :The complement of an event is the event not occurring.

Step 6 :In this case, drawing all hearts (Event A) and drawing no face cards (Event B) are not mutually exclusive, because it's possible to draw a heart that is not a face card.

Step 7 :They are not complements, because it's possible for neither event to occur (for example, if Michelle draws all diamonds).

Step 8 :However, whether or not Michelle draws a heart does not affect whether or not she draws a face card, and vice versa. Therefore, the events are independent.

Step 9 :Final Answer: \(\boxed{\text{independent}}\).

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