Mutually Exclusive and Non-Mutually Exclusive Events worksheet ... - Free Printable

Let's solve each problem step by step, determining whether the events are mutually exclusive or non-mutually exclusive, and then calculating the probability in simplest form.

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🔹 Background:

A standard deck has 52 cards:
- 4 suits: Hearts (♥), Diamonds (♦) – Red
- Spades (♠), Clubs (♣) – Black
- Each suit has 13 cards: A, 2–10, J, Q, K

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## ✔ Definitions:

- Mutually Exclusive Events: Two events that cannot happen at the same time.
Example: Drawing a king and an ace — you can't draw both on one card.

- Non-Mutually Exclusive Events: Two events that can happen together.
Example: Drawing a heart and a jack — the Jack of Hearts satisfies both.

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🟦 Problem 1: A king or an ace?

- Are they mutually exclusive?
→ Yes. A card cannot be both a king and an ace.
So, Mutually Exclusive

- Number of kings: 4
- Number of aces: 4
- Total favorable outcomes: 4 + 4 = 8

- Probability = $ \frac{8}{52} = \frac{2}{13} $

✔ Answer:
Mutually Exclusive
Probability: $ \frac{2}{13} $

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🟦 Problem 2: A heart or a jack?

- Are they mutually exclusive?
→ No. The Jack of Hearts is both a heart and a jack.
So, Non-Mutually Exclusive

- Use formula:
$ P(A \cup B) = P(A) + P(B) - P(A \cap B) $

- Number of hearts: 13
- Number of jacks: 4
- Jack of hearts: 1 (overlap)

- Favorable outcomes: 13 + 4 - 1 = 16

- Probability = $ \frac{16}{52} = \frac{4}{13} $

✔ Answer:
Non-Mutually Exclusive
Probability: $ \frac{4}{13} $

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🟦 Problem 3: A black card or 10 of spades?

- Are they mutually exclusive?
→ No. The 10 of spades is a black card, so it's included in both.

But we’re asking for "a black card OR the 10 of spades". Since the 10 of spades is already part of black cards, adding it again would cause double-counting.

- However, note: “or” includes all black cards AND the 10 of spades, but since 10 of spades is already black, this just means all black cards.

So total favorable = number of black cards = 26 (spades + clubs)

- But wait: Is there overlap? Yes — the 10 of spades is already in black cards.

- So:
- Black cards: 26
- 10 of spades: 1 (already counted)
- So total unique cards = 26

- Probability = $ \frac{26}{52} = \frac{1}{2} $

But let’s use the formula to confirm:

$ P(\text{black}) + P(10\spadesuit) - P(\text{both}) = \frac{26}{52} + \frac{1}{52} - \frac{1}{52} = \frac{26}{52} = \frac{1}{2} $

✔ Answer:
Non-Mutually Exclusive
Probability: $ \frac{1}{2} $

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🟦 Problem 4: A red card or a club?

- Are they mutually exclusive?
→ No. Clubs are black, so no red club exists.
But "red card" and "club" have no overlap because clubs are black.

So actually, they are mutually exclusive?

Wait: Let's think carefully.

- Red cards: Hearts and Diamonds → 26 cards
- Club cards: 13 cards, all black

→ No card is both red and a club → No overlap

So: Mutually Exclusive

- Red cards: 26
- Clubs: 13
- Total favorable: 26 + 13 = 39

- Probability = $ \frac{39}{52} = \frac{3}{4} $

✔ Answer:
Mutually Exclusive
Probability: $ \frac{3}{4} $

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🟦 Problem 5: A king or an even number?

- Are they mutually exclusive?
→ No. A king is not a number, but even-numbered cards include 2, 4, 6, 8, 10.

Can a card be both a king and an even number?
→ No. Kings are face cards, not numbered.

So: Mutually Exclusive

But wait — what about the king of even-numbered rank? There is no such thing. All kings are face cards.

So no card is both a king and an even-numbered card.

So: Mutually Exclusive

Now count:

- Number of kings: 4
- Even-numbered cards: 2, 4, 6, 8, 10 → 5 values × 4 suits = 20 cards

- Total favorable: 4 + 20 = 24

- Probability = $ \frac{24}{52} = \frac{6}{13} $

✔ Answer:
Mutually Exclusive
Probability: $ \frac{6}{13} $

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## ✔ Final Answers:

| Question | Type | Probability |
|--------|------|-------------|
| 1. A king or an ace? | Mutually Exclusive | $ \frac{2}{13} $ |
| 2. A heart or a jack? | Non-Mutually Exclusive | $ \frac{4}{13} $ |
| 3. A black card or 10 of spades? | Non-Mutually Exclusive | $ \frac{1}{2} $ |
| 4. A red card or a club? | Mutually Exclusive | $ \frac{3}{4} $ |
| 5. A king or an even number? | Mutually Exclusive | $ \frac{6}{13} $ |

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✔ Summary of Fill-in-the-Blanks:

1. Mutually Exclusive → Probability: $ \frac{8}{52} = \boxed{\frac{2}{13}} $
2. Non-Mutually Exclusive → Probability: $ \frac{16}{52} = \boxed{\frac{4}{13}} $
3. Non-Mutually Exclusive → Probability: $ \frac{26}{52} = \boxed{\frac{1}{2}} $
4. Mutually Exclusive → Probability: $ \frac{39}{52} = \boxed{\frac{3}{4}} $
5. Mutually Exclusive → Probability: $ \frac{24}{52} = \boxed{\frac{6}{13}} $

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Let me know if you'd like this filled into the worksheet format! 😊