Suppose you draw a card from an ordinary deck of playing cards What are the odds in favor of drawing a face card?

b. What are the odds against drawing a face card?

a. 12/52

b. 1 -12/52

To determine the odds in favor of drawing a face card, we need to first find the number of favorable outcomes (face cards) and the number of possible outcomes (total number of cards in the deck).

Here's how to do it:

1. Find the number of favorable outcomes (face cards):
A standard deck of playing cards has 4 face cards in each of the 4 suits (hearts, diamonds, clubs, and spades). So, there are a total of 4 face cards in each suit, resulting in a total of 4 x 4 = 16 face cards in the entire deck.

2. Find the number of possible outcomes (total number of cards in the deck):
A standard deck of playing cards has a total of 52 cards, including 4 suits (hearts, diamonds, clubs, and spades) with each suit having 13 cards (including face cards and numbered cards).

3. Calculate the odds in favor of drawing a face card:
The odds in favor of an event are determined by dividing the number of favorable outcomes by the number of possible outcomes.
In this case, the odds in favor of drawing a face card would be:
Number of favorable outcomes / Number of possible outcomes = 16 / 52

Simplifying the fraction, we get:
4 / 13

So, the odds in favor of drawing a face card are 4/13.

To find the odds against drawing a face card, we can simply subtract the odds in favor from 1 since the sum of the odds in favor and the odds against is always equal to 1.

Odds against drawing a face card = 1 - Odds in favor of drawing a face card
Odds against drawing a face card = 1 - 4/13

To simplify the fraction, we find a common denominator:
13/13 - 4/13 = 9/13

So, the odds against drawing a face card are 9/13.

To find the odds in favor of drawing a face card, we need to determine the number of favorable outcomes (drawing a face card) and the number of unfavorable outcomes (not drawing a face card).

a. Number of favorable outcomes (face cards): There are 12 face cards in a deck (4 kings, 4 queens, and 4 jacks).

b. Number of unfavorable outcomes (non-face cards): There are 40 non-face cards in a deck.

a. Odds in favor of drawing a face card: The odds in favor can be calculated as the number of favorable outcomes divided by the number of unfavorable outcomes.

Odds in favor = Number of favorable outcomes / Number of unfavorable outcomes
Odds in favor = 12 / 40
Odds in favor = 3 / 10 or 0.3

So, the odds in favor of drawing a face card are 3 to 10 or 0.3.

b. Odds against drawing a face card: The odds against can be calculated as the number of unfavorable outcomes divided by the number of favorable outcomes.

Odds against = Number of unfavorable outcomes / Number of favorable outcomes
Odds against = 40 / 12
Odds against = 10 / 3 or approximately 3.33

So, the odds against drawing a face card are approximately 10 to 3 or 3.33.