You randomly select one card from a​ 52-card deck.  Find the probability of selecting a five or a six.

To find the probability of selecting a five or a six from a 52-card deck, follow these steps:

1. **Total number of cards**: There are 52 cards in a standard deck.

2. **Number of fives in the deck**: There are 4 fives (one from each suit: hearts, diamonds, clubs, and spades).

3. **Number of sixes in the deck**: There are also 4 sixes (one from each suit: hearts, diamonds, clubs, and spades).

4. **Total number of favorable outcomes**: Since you can select either a five or a six, the total number of favorable outcomes is the sum of the number of fives and the number of sixes:

\[
4 \text{ (fives)} + 4 \text{ (sixes)} = 8 \text{ favorable outcomes}
\]

5. **Probability of selecting a five or a six**: The probability is given by the ratio of the number of favorable outcomes to the total number of cards:

\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of cards}} = \frac{8}{52}
\]

6. **Simplify the fraction**:

\[
\frac{8}{52} = \frac{2}{13}
\]

Thus, the probability of selecting a five or a six is **\(\frac{2}{13}\)**.

Would you like more details or have any questions?

Here are 8 related questions for further exploration:

1. What is the probability of selecting a five, six, or seven?
2. What is the probability of selecting a face card (Jack, Queen, or King)?
3. What is the probability of selecting a red card (hearts or diamonds)?
4. What is the probability of selecting a card that is either a heart or a spade?
5. What is the probability of selecting an Ace?
6. If two cards are selected, what is the probability that both are fives?
7. What is the probability of selecting a card that is not a face card?
8. What is the probability of selecting a card that is either a three or a four?

**Tip**: When calculating the probability of either of two mutually exclusive events (like selecting a five or a six), simply add the probabilities of each individual event.

Discover how to calculate the probability of selecting a five or a six from a standard 52-card deck. This problem explores basic probability concepts, including the counting principle and calculating favorable outcomes. Suitable for students in Grades 6-8.

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