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 diamond or 6?
well, how many of the cards are diamonds or 6's?
To find the probability of selecting a diamond or 6 from a well-shuffled standard deck of 52 cards, we need to determine the number of favorable outcomes and the total number of possible outcomes.
1. Determine the number of favorable outcomes:
- There are four suits in a deck, and one of them is diamonds. So, there are 13 diamonds in total.
- Additionally, there are four 6s in the deck (one for each suit).
- However, we need to subtract the one case where the 6 of diamonds is already counted as a diamond.
- Therefore, the total number of favorable outcomes is 13 + 4 - 1 = 16.
2. Determine the total number of possible outcomes:
- A standard deck of 52 cards contains four suits (diamonds, clubs, hearts, and spades) with 13 cards each.
- Therefore, the total number of possible outcomes is 52.
3. Calculate the probability:
- The probability of an event happening is given by the formula: favorable outcomes / total outcomes.
- In this case, the probability is: 16 / 52 = 4 / 13 ≈ 0.3077, or approximately 30.77%.
So, the probability of randomly selecting a card that is either a diamond or 6 from a well-shuffled standard deck is approximately 30.77%.