Two cards are selected without replacement from a standard deck of 52 cards. What is the probability that the first card selected is either red or a face card?
What we don't want is a selection with no face cards or red cards.
If we take all the reds and facecards out, there would be 30 cards left.
so if we find the prob of getting 2 of those cards
= 30/52 x 29/51 = 145/442
So the prob of the stated problem = 1 - 145/442 = 297/442
I misread your question.
It is actually easier than the one I answered.
Since there are 22 cards that are either red or face cards in the deck, the prob(red or face) on the first draw = 22/52 = 11/26
(Why are you stating that there are 2 cards drawn, and why are you stating replacement conditions, if all you are interested in is the first card?)
Thank you! I understand now. The probability is actually 8/13, but you definitely had the right idea. Thanks again!
To find the probability that the first card selected is either red or a face card, we need to determine the total number of favorable outcomes and the total number of possible outcomes.
Step 1: Calculate the total number of favorable outcomes.
First, we need to determine the number of red cards in a standard deck. There are 26 red cards (13 hearts and 13 diamonds) in a deck of 52 cards.
Next, we need to determine the number of face cards in a standard deck. There are 12 face cards (3 face cards for each of the 4 suits: hearts, diamonds, clubs, and spades).
However, we need to make sure that we do not count the red face cards twice. Among the 12 face cards, 6 are red (3 hearts and 3 diamonds). So, the number of face cards that are not red is 12 - 6 = 6.
To find the total number of favorable outcomes, we add the number of red cards and the number of face cards that are not red: 26 + 6 = 32.
Step 2: Calculate the total number of possible outcomes.
When the first card is chosen, there are 52 cards in the deck.
So, the total number of possible outcomes is 52.
Step 3: Calculate the probability.
Finally, we can calculate the probability by dividing the total number of favorable outcomes by the total number of possible outcomes.
Probability = Favorable outcomes / Possible outcomes
= 32 / 52
= 8 / 13
≈ 0.615
Therefore, the probability that the first card selected is either red or a face card is approximately 0.615, or 61.5%.