One card is selected from a deck of cards. Find the probability of selecting a red card or a card less than 4 .
(Note: The ace is considered a low card.)
There are 52 cards in a deck.
There are 26 red cards in a deck (all hearts and diamonds).
There are 12 cards less than 4 in a deck (all aces, twos and threes).
Compute the appropriate ratios.
Well, well, well, it seems we have a probability question here! Let's dive right into it, shall we?
To find the probability of selecting a red card or a card less than 4, we'll need to first determine how many cards satisfy these conditions.
First, let's consider the red cards: In a standard deck, there are 26 red cards (13 hearts and 13 diamonds).
Now, let's think about the cards less than 4: We have the ace, 2, and 3 in each suit, totaling to 12 cards.
But hold your horses! We need to be careful not to double count the cards that are both red and less than 4. Luckily, there are no such cards in this case. Phew!
So, to calculate the total number of cards that satisfy our condition, we add the number of red cards and the number of cards less than 4: 26 + 12 = 38.
And since there are 52 cards in a deck, the probability of selecting a red card or a card less than 4 is 38/52, which can be simplified to 19/26.
So, my funny friend, the probability is 19/26. I hope that answer tickled your funny bone!
To find the probability of selecting a red card or a card less than 4, we need to calculate the individual probabilities of each event and then sum them.
Step 1: Determine the number of favorable outcomes for each event:
- Number of red cards in a standard deck of cards: There are 26 red cards, consisting of 13 hearts and 13 diamonds.
- Number of cards less than 4 in a standard deck of cards: There are 3 cards less than 4 in each of the four suits (Aces and numbered cards 2 and 3), totaling 12 cards.
Step 2: Determine the total number of outcomes:
A standard deck of cards contains 52 cards.
Step 3: Calculate the probability of each event:
The probability of selecting a red card = Number of red cards / Total number of cards = 26/52 = 1/2.
The probability of selecting a card less than 4 = Number of cards less than 4 / Total number of cards = 12/52 = 3/13.
Step 4: Calculate the probability of the union of the two events (selecting a red card or a card less than 4):
The probability of the union of two events = P(red card) + P(card less than 4) - P(red card and card less than 4).
To avoid double-counting, we subtract the intersection of the two events.
The probability of selecting a red card and a card less than 4 is 2/52 since there are only two red cards that are less than 4 (the two red 3s).
P(red card or card less than 4) = P(red card) + P(card less than 4) - P(red card and card less than 4)
= 1/2 + 3/13 - 2/52
= 13/26 + 6/26 - 2/52
= 19/26 - 2/52
= 19/26 - 1/26
= 18/26
= 9/13
Therefore, the probability of selecting a red card or a card less than 4 is 9/13.
To find the probability of selecting a red card or a card less than 4 from a deck of cards, we need to determine the total number of favorable outcomes and divide it by the total number of possible outcomes.
Number of favorable outcomes:
A red card can be either a heart or a diamond. In a standard deck of playing cards, there are 26 red cards (13 hearts and 13 diamonds).
For cards less than 4, we need to consider the ace, 2, and 3. There are two red aces (Ace of Hearts and Ace of Diamonds), two red twos, and two red threes. So, there are a total of 6 cards less than 4.
Number of possible outcomes:
A standard deck of playing cards contains 52 cards.
Now we can calculate the probability:
Probability = (Number of favorable outcomes) / (Number of possible outcomes)
Probability = (26 + 6) / 52
Probability = 32 / 52
Probability ≈ 0.615
So, the probability of selecting a red card or a card less than 4 is approximately 0.615, or 61.5%.