what is the probability of drawing a red card or a face card in a standard deck of 52?enter your answer as a fraction in the form of a/b for example 1/2
there are 26 reds and another 6 black face cards, so
32/52 = 8/13
To calculate the probability of drawing a red card or a face card in a standard deck of 52, we need to determine the number of favorable outcomes (red cards or face cards) and divide it by the total number of possible outcomes (all 52 cards).
Let's break it down:
1. Counting the red cards:
In a standard deck, there are 26 red cards (13 hearts and 13 diamonds).
2. Counting the face cards:
Face cards include the Jacks, Queens, and Kings. There are 3 face cards in each suit (Hearts, Diamonds, Clubs, and Spades), resulting in a total of 12 face cards in the deck.
3. Counting the red face cards:
Out of the 12 face cards, 6 of them are red (3 hearts and 3 diamonds).
4. Calculating the favorable outcomes:
We need to add the count of red cards (26) and the count of red face cards (6) to get the total number of favorable outcomes:
26 + 6 = 32
5. Calculating the total number of outcomes:
In a standard deck of 52 cards, there are 52 possible outcomes.
Now we can calculate the probability as the ratio of favorable outcomes to total outcomes:
Probability = Favorable Outcomes / Total Outcomes
Probability = 32 / 52
Simplifying the fraction, we get the probability as 8/13.
Therefore, the answer is 8/13.
To find the probability of drawing a red card or a face card in a standard deck of 52, we need to calculate the number of favorable outcomes (red cards or face cards) divided by the total number of possible outcomes (all cards in the deck).
First, let's determine the number of red cards in a deck. There are 26 red cards in total (13 hearts + 13 diamonds).
Next, let's calculate the number of face cards in a deck. There are 12 face cards in total (3 face cards in each suit: jack, queen, king).
However, we need to be careful not to count the cards that are both red and face cards (red face cards). There are 6 red face cards in total (2 red jacks + 2 red queens + 2 red kings).
Now we can calculate the total number of favorable outcomes by adding the number of red cards (26) and face cards (12), and then subtracting the number of red face cards (6).
Total number of favorable outcomes = 26 + 12 - 6 = 32
Finally, the probability can be calculated as the number of favorable outcomes divided by the total number of possible outcomes:
Probability = Favorable outcomes / Total outcomes
Probability = 32 / 52
Hence, the probability of drawing a red card or a face card in a standard deck of 52 is 8/13.