One card is selected from a deck of cards. Determine the probability of selecting a jack or a red card ?
number of Jacks = 4
number of red cards = 26 , of which 2 are Jacks
so Jacks or red cards = 26 + 4-2 = 28
prob(Jack or red) = 28/52 = 7/13
Oh, probability, huh? Well, let's do some card math! So, in a standard deck of cards, there are 52 cards. Out of those, there are 4 jacks: the Jack of Hearts, Clubs, Diamonds, and Spades. And since we're also looking for red cards, well, half of the deck is red. That's 26 red cards.
Now, out of those 26 red cards, 2 of them are jacks: the Jack of Hearts and the Jack of Diamonds.
So, to find the probability of selecting a jack or a red card, we add up the number of favorable outcomes (6) and divide it by the total number of possible outcomes (52).
Probability = 6/52
Simplified, that's 3/26.
So, the probability of selecting a jack or a red card is about 3/26. And if you ask me, that's a pretty good chance!
To determine the probability of selecting a jack or a red card from a standard deck of 52 cards, we need to count the number of favorable outcomes and divide it by the total number of possible outcomes.
1. Counting the favorable outcomes:
- There are 4 jacks in a deck (one of each suit: hearts ♥, diamonds ♦, clubs ♣, spades ♠).
- There are 26 red cards in a deck (13 hearts ♥ and 13 diamonds ♦).
- However, we need to subtract one jack (the jack of hearts ♥) from the count of red cards because it is already counted as a jack.
- So, the total number of favorable outcomes is 4 + 26 - 1 = 29.
2. Counting the total number of possible outcomes:
- In a standard deck, there are 52 cards.
3. Calculating the probability:
- Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
- Probability = 29 / 52
- Probability = 0.5577
Therefore, the probability of selecting a jack or a red card from a deck is approximately 0.558 or 55.8%.
To determine the probability of selecting a jack or a red card from a deck of cards, we need to first count the number of jacks and the number of red cards in the deck.
A standard deck of playing cards contains 52 cards in total, divided into 4 suits (hearts, diamonds, clubs, and spades) with each suit having 13 cards (ace, 2-10, jack, queen, and king).
There are 4 jacks in the deck, one in each suit. Additionally, there are 26 red cards in the deck, which comprises the 13 hearts and the 13 diamonds. Since the jack of hearts and the jack of diamonds are both red cards and jacks, we need to ensure we don't count them twice.
So, the number of jacks or red cards in the deck is calculated as:
Number of jacks + Number of red cards - Number of jacks and red cards = 4 + 26 - 2 = 28
Thus, there are 28 cards that are either jacks or red cards in the deck.
Finally, we calculate the probability by dividing the number of favorable outcomes (selecting a jack or a red card) by the total number of possible outcomes (selecting any card from the deck):
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 28 / 52
Simplifying the fraction, we get:
Probability = 7 / 13
Therefore, the probability of selecting a jack or a red card from a deck of cards is 7/13.