If you randomly select a card from a well-shuffled standard deck of 52 cards, what is the probability that the card you select is a heart or 10?
16/52 = 4/13
To determine the probability of selecting a heart or a 10 from a well-shuffled standard deck of 52 cards, we need to first calculate the number of favorable outcomes (number of hearts or 10s) and the total number of possible outcomes (total number of cards in the deck).
1. Number of favorable outcomes:
- There are 13 hearts in a standard deck (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King).
- There are 3 additional 10s (10 of diamonds, 10 of clubs, 10 of spades) in the deck.
- So, the number of favorable outcomes is 13 (hearts) + 3 (10s) = 16.
2. Total number of possible outcomes:
- There are 52 cards in a standard deck.
3. Probability calculation:
- Probability = Number of favorable outcomes / Total number of possible outcomes
- Probability = 16 / 52
- Simplifying the fraction, we get: Probability = 4 / 13.
Therefore, the probability of randomly selecting a card that is a heart or a 10 from a well-shuffled standard deck is 4/13.
To calculate the probability of selecting a heart or a 10 from a well-shuffled standard deck of 52 cards, we need to determine the number of favorable outcomes (cards that are hearts or 10s) and divide it by the total number of possible outcomes (all the cards in the deck).
First, let's identify how many favorable outcomes there are:
1. Hearts: A standard deck contains 13 hearts (one for each rank: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King).
2. 10s: There are four 10s in the deck (one for each suit: hearts, diamonds, clubs, and spades).
However, since the question is asking for the probability of selecting a heart or a 10, we need to be aware that one card, the 10 of hearts, satisfies both conditions. Therefore, we must not count it twice. Thus, the total number of favorable outcomes is 13 (hearts) + 4 (10s) - 1 (10 of hearts) = 16.
Second, we need to determine the total number of possible outcomes, which is the number of cards in a standard deck: 52.
Now we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Favorable outcomes / Total number of outcomes
Probability = 16 / 52
Probability ≈ 0.3077
Therefore, the probability of randomly selecting a card that is either a heart or a 10 from a well-shuffled standard deck is approximately 0.3077, or about 30.77%.