When a single card is drawn from a shuffled deck of cards, find the odds against getting a 9.
To find the odds against getting a 9 when drawing a single card from a shuffled deck of cards, we first need to determine the number of favorable outcomes and the number of possible outcomes.
In a standard deck of 52 playing cards, there are four 9s (one in each suit: hearts, diamonds, clubs, and spades). So, the number of favorable outcomes (getting a 9) is 4.
The number of possible outcomes is the total number of cards in the deck, which is 52.
Therefore, the odds against getting a 9 can be calculated by comparing the unfavorable outcomes (non-9s) to the favorable outcomes.
Number of unfavorable outcomes = Total outcomes - Favorable outcomes
Number of unfavorable outcomes = 52 - 4 = 48.
So, the odds against getting a 9 can be expressed as 48 to 4 or 48:4. Simplifying the ratio gives 12 to 1 or 12:1.
The odds against getting a 9 when drawing a single card from a shuffled deck of cards are 12 to 1.