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 club or 10? (Your answer must be in the form of a reduced fraction.)




A standard deck of 52 cards contains:

- 13 clubs (one for each rank: Ace, 2, 3, ..., 10, Jack, Queen, King),
- 1 additional card that is a 10 but not a club (there are three 10s remaining: 10 of hearts, 10 of diamonds, 10 of spades).

Thus, we have:

- 13 clubs,
- 3 additional 10s.

However, the 10 of clubs is included in both categories, so we must count it only once. Therefore, the total number of favorable outcomes is:
\[
13 + 3 - 1 = 15
\]

The total number of possible outcomes is 52 (the total number of cards in the deck).

Thus, the probability of selecting a club or a 10 is:
\[
\frac{15}{52}
\]

This fraction is already in its simplest form.

**Answer:** The probability is \( \frac{15}{52} \).

Would you like any further details or have questions?

Here are 5 related questions for you to consider:
1. What is the probability of drawing a face card (Jack, Queen, or King) from a standard deck?
2. What is the probability of drawing a red card or an Ace?
3. How many possible outcomes are there for drawing two cards, both being hearts?
4. What is the probability of drawing a spade or a number card (2–10)?
5. How many cards in a deck are both red and numbered from 2 to 10?

**Tip:** When calculating probabilities with overlapping conditions, remember to subtract the overlap to avoid double-counting.

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 club or 10?

Find out the probability of selecting a club or 10 from a standard deck of 52 cards. This problem involves basic probability rules and set theory, showing how to account for overlapping events. Suitable for Grades 6-8 students.

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