A Card Is Drawn From A Well-shuffled Deck Of 52 Cards. Find $P$ (drawing An Ace Or An 8).a. $\frac{8}{13}$ B. $\frac{2}{13}$ C. $\frac{4}{13}$ D. $\frac{13}{2}$ Please Select The Best Answer From The
A Card is Drawn from a Well-Shuffled Deck of 52 Cards: Finding the Probability of Drawing an Ace or an 8
In this article, we will explore the concept of probability and how it applies to drawing a card from a well-shuffled deck of 52 cards. We will specifically focus on finding the probability of drawing an ace or an 8. Probability is a measure of the likelihood of an event occurring, and it is calculated as the number of favorable outcomes divided by the total number of possible outcomes.
Understanding the Deck of Cards
A standard deck of cards consists of 52 cards, divided into four suits: hearts, diamonds, clubs, and spades. Each suit contains 13 cards: ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, and king. In this problem, we are interested in drawing an ace or an 8.
Calculating the Probability
To calculate the probability of drawing an ace or an 8, we need to count the number of favorable outcomes and divide it by the total number of possible outcomes.
- The total number of possible outcomes is 52, since there are 52 cards in the deck.
- The number of favorable outcomes is the number of aces and 8s in the deck. There are 4 aces (one in each suit) and 4 8s (one in each suit), so the total number of favorable outcomes is 4 + 4 = 8.
Applying the Formula
Now that we have the number of favorable outcomes and the total number of possible outcomes, we can apply the formula for probability:
P(event) = Number of favorable outcomes / Total number of possible outcomes
In this case, the event is drawing an ace or an 8. The number of favorable outcomes is 8, and the total number of possible outcomes is 52. Therefore, the probability of drawing an ace or an 8 is:
P(drawing an ace or an 8) = 8/52 = 2/13
In conclusion, the probability of drawing an ace or an 8 from a well-shuffled deck of 52 cards is 2/13. This is a relatively low probability, indicating that it is less likely to draw an ace or an 8 than other cards in the deck.
The correct answer is:
b.
A Card is Drawn from a Well-Shuffled Deck of 52 Cards: Q&A
In our previous article, we explored the concept of probability and how it applies to drawing a card from a well-shuffled deck of 52 cards. We specifically focused on finding the probability of drawing an ace or an 8. In this article, we will answer some frequently asked questions related to this topic.
Q: What is the probability of drawing a specific card from a well-shuffled deck of 52 cards?
A: The probability of drawing a specific card from a well-shuffled deck of 52 cards is 1/52, since there is only one specific card in the deck.
Q: How many aces are there in a standard deck of cards?
A: There are 4 aces in a standard deck of cards, one in each suit: hearts, diamonds, clubs, and spades.
Q: How many 8s are there in a standard deck of cards?
A: There are 4 8s in a standard deck of cards, one in each suit: hearts, diamonds, clubs, and spades.
Q: What is the probability of drawing an ace of hearts from a well-shuffled deck of 52 cards?
A: The probability of drawing an ace of hearts from a well-shuffled deck of 52 cards is 1/52, since there is only one ace of hearts in the deck.
Q: What is the probability of drawing a card that is not an ace or an 8 from a well-shuffled deck of 52 cards?
A: To find the probability of drawing a card that is not an ace or an 8, we need to count the number of cards that are not aces or 8s and divide it by the total number of possible outcomes. There are 52 cards in the deck, and 8 of them are aces or 8s, so there are 52 - 8 = 44 cards that are not aces or 8s. The probability of drawing a card that is not an ace or an 8 is therefore 44/52 = 11/13.
Q: Can the probability of drawing an ace or an 8 be affected by the order in which the cards are drawn?
A: No, the probability of drawing an ace or an 8 is not affected by the order in which the cards are drawn. The probability of drawing an ace or an 8 is determined by the number of aces and 8s in the deck, and this number does not change regardless of the order in which the cards are drawn.
Q: Is it possible to draw two aces in a row from a well-shuffled deck of 52 cards?
A: Yes, it is possible to draw two aces in a row from a well-shuffled deck of 52 cards. The probability of drawing two aces in a row is (1/52) × (3/51), since there are 3 aces remaining in the deck after the first ace is drawn.
Q: Is it possible to draw two 8s in a row from a well-shuffled deck of 52 cards?
A: Yes, it is possible to draw two 8s in a row from a well-shuffled deck of 52 cards. The probability of drawing two 8s in a row is (1/52) × (3/51), since there are 3 8s remaining in the deck after the first 8 is drawn.
In conclusion, we have answered some frequently asked questions related to drawing a card from a well-shuffled deck of 52 cards. We have discussed the probability of drawing a specific card, the number of aces and 8s in a standard deck of cards, and the probability of drawing two aces or two 8s in a row.