Probability worksheet using a deck of cards to calculate various probabilities.

Let’s solve each probability problem step by step. We’re using a standard 52-card deck (no jokers). That means:

- 4 suits: Hearts, Diamonds, Clubs, Spades → 13 cards per suit
- Colors: Red (Hearts, Diamonds), Black (Clubs, Spades) → 26 red, 26 black
- Face cards: Jack, Queen, King → 3 per suit × 4 suits = 12 face cards total
- Numbered cards: Ace through 10 in each suit → but note: sometimes “Ace” is not considered a number card; however, for this worksheet, we’ll assume “number card” means 2 through 10 (9 per suit × 4 = 36), unless specified otherwise. But let’s check context — question #7 says “face card”, and #8 says “2 of Diamonds”, so likely “number card” here includes Ace? Wait — actually, in many school contexts, “number card” excludes face cards and Aces. Let’s clarify based on common usage in such worksheets.

Actually, looking at question #7: “Find the probability of drawing a face card.” → So face cards are J, Q, K.

Question #8: “drawing a 2 of Diamonds” → specific card.

Question #9: “Diamond 5 through 10” → that’s 6 cards: 5,6,7,8,9,10 of Diamonds.

Question #10: “cards 3 through 7” → probably all suits? Or just one suit? The wording is ambiguous, but since it doesn’t specify suit, it likely means any card with rank 3,4,5,6,7 across all suits → 5 ranks × 4 suits = 20 cards.

Also, question #5: “black card” → 26 black cards.

Question #6: “red cards 2 through 7” → red suits are Hearts and Diamonds. In each red suit, cards 2,3,4,5,6,7 → 6 cards per suit × 2 suits = 12 cards.

Question #3: “Spade” → 13 spades.

Question #4: “a 5” → there are four 5s (one per suit).

Question #1: “Diamond” → 13 diamonds.

Question #2: “face card that is black” → black suits are Clubs and Spades. Each has 3 face cards → 3×2=6 black face cards.

Now let’s compute each probability as fraction over 52, then simplify if needed.

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1. Probability of drawing a Diamond

→ 13 diamonds out of 52 cards
→ 13/52 = 1/4

2. Probability of drawing a face card that is black

→ Black face cards: J,Q,K of Clubs and Spades → 3×2 = 6
→ 6/52 = 3/26

3. Probability of drawing a Spade

→ 13 spades
→ 13/52 = 1/4

4. Probability of drawing a 5

→ Four 5s (one per suit)
→ 4/52 = 1/13

5. Probability of drawing a black card

→ 26 black cards
→ 26/52 = 1/2

6. Probability of drawing red cards 2 through 7

→ Red suits: Hearts, Diamonds
→ In each: 2,3,4,5,6,7 → 6 cards
→ Total: 6×2 = 12
→ 12/52 = 3/13

7. Probability of drawing a face card

→ 12 face cards total (J,Q,K × 4 suits)
→ 12/52 = 3/13

8. Probability of drawing a 2 of Diamonds

→ Only ONE such card
→ 1/52

9. Probability of drawing a Diamond 5 through 10

→ Diamonds: 5,6,7,8,9,10 → 6 cards
→ 6/52 = 3/26

10. Probability of drawing cards 3 through 7

→ Assuming this means ANY card with rank 3,4,5,6,7 (all suits)
→ 5 ranks × 4 suits = 20 cards
→ 20/52 = 5/13

*(Note: If it meant only one suit, it would say “in a suit” or similar — but since it doesn’t, and other questions specify suit when needed, we go with all suits.)*

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Final Answer:

1. 1/4
2. 3/26
3. 1/4
4. 1/13
5. 1/2
6. 3/13
7. 3/13
8. 1/52
9. 3/26
10. 5/13