Problem

One card is randomly selected from a deck of cards. Find the odds against drawing a spade greater than 4 and less than 9 .
The odds against drawing a spade greater than 4 and less than 9 are (Simplify your answer.)

Answer

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Answer

Final Answer: The odds against drawing a spade greater than 4 and less than 9 are \(\boxed{12}\).

Steps

Step 1 :The deck of cards has 52 cards in total, with 13 cards of each suit (hearts, diamonds, clubs, spades).

Step 2 :The spades greater than 4 and less than 9 are 5, 6, 7, 8, which are 4 cards.

Step 3 :So, the odds against drawing a spade greater than 4 and less than 9 are the total number of cards minus the number of favorable outcomes, divided by the number of favorable outcomes.

Step 4 :\(\text{total_cards} = 52\)

Step 5 :\(\text{favorable_outcomes} = 4\)

Step 6 :\(\text{odds_against} = \frac{\text{total_cards} - \text{favorable_outcomes}}{\text{favorable_outcomes}} = 12.0\)

Step 7 :Final Answer: The odds against drawing a spade greater than 4 and less than 9 are \(\boxed{12}\).

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