Worksheet on identifying independent and dependent events in probability.

To determine whether events are dependent or independent, we need to ask: Does the outcome of the first event affect the probability of the second event?

- Independent events: The result of one does NOT change the chances for the other. (Example: Flipping a coin twice — the first flip doesn’t change the 50/50 chance on the second.)
- Dependent events: The result of the first DOES change the chances for the second. (Example: Drawing cards without replacing them — if you take out an Ace, there’s one less Ace left in the deck.)

Let’s go through each problem:

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1) You choose a green marble from a bag, put it back in the bag, and then choose a red marble.
→ Since you put the first marble back, the total number of marbles stays the same. The second draw is not affected by the first.
✔ Independent

2) Flipping a coin, getting tails, and rolling a 6 on a die.
→ Coin flips and dice rolls don’t affect each other at all.
✔ Independent

3) Randomly taking a piece of dark chocolate from a box of Halloween chocolates, eating it, then randomly taking a piece of milk chocolate.
→ You ate the first piece, so it’s gone. That changes what’s left in the box. The second choice depends on what was removed.
✔ Dependent

4) Spinning a spinner landing on a 6, and rolling a 2 on a die.
→ Spinner and die are separate things. One doesn’t affect the other.
✔ Independent

5) Spinning a spinner twice and getting an even number both times.
→ Each spin is separate. Getting an even number the first time doesn’t change the odds for the second spin.
✔ Independent

6) Choosing a king from a deck of cards, keeping it, and then choosing a Queen.
→ You kept the King, so now there are only 51 cards left. The chance of drawing a Queen is now slightly different because the deck changed.
✔ Dependent

7) There are 2 math books and 3 social studies books on a shelf. Randomly choosing a math book off the shelf, giving it to your friend, and then randomly choosing another math book.
→ You gave away the first math book, so now there’s only 1 math book left (and still 3 social studies). The second pick is affected.
✔ Dependent

8) Randomly choosing a pink colored pencil from a box of pencils, putting it into the eraser, and then choosing a purple pencil.
→ Wait — “putting it into the eraser”? That seems like a typo. Probably meant “putting it back” or “removing it”. But since it says “putting it into the eraser”, that likely means you’re removing it from the box (you can’t use it anymore). So the box has one less pencil. Second choice is affected.
✔ Dependent *(Assuming "putting it into the eraser" means removing it from available pencils)*

> ⚠️ Note: If this was meant to say “putting it back”, then it would be independent. But as written, “into the eraser” implies removal → dependent.

9) You have a full deck of cards. You choose a card, look at it and then choose another without putting the first card back. The first card was a 9 and the second was an 8.
→ You didn’t put the first card back → deck size decreased → second draw affected.
✔ Dependent

10) You have a full deck of cards. You choose a card, look at it and then choose another without putting the first card back. The first card was a 9 and the second card was an 8.
→ Same as #9! Just reworded. Still no replacement → dependent.
✔ Dependent

Wait — actually, looking again: #9 and #10 are identical? Let me check the original text...

Actually, rereading:

#9: “You have a full deck of cards. You choose a card, look at it and then choose another without putting the first card back. The first card was a 9 and the second was an 8.”

#10: “You have a full deck of cards. You choose a card, look at it and then choose another without putting the first card back. The first card was a 9 and the second card was an 8.”

They are word-for-word the same. Probably a duplication error in the worksheet. But regardless, both describe sampling without replacement → dependent.

But let’s assume maybe #10 was meant to say “with replacement”? No — it clearly says “without putting the first card back” in both.

So both are dependent.

However, perhaps there’s a trick? Let’s read carefully:

In #9: “The first card was a 9 and the second was an 8.” → This is describing what happened, but the key is the method: “without putting the first card back” → so dependent.

Same for #10.

So both are dependent.

But wait — maybe the question is testing if you notice they’re the same? Or perhaps it’s a copy-paste error. Either way, based on description, both are dependent.

Alternatively, maybe #10 was supposed to say “with replacement”? But it doesn’t. We must go by what’s written.

Final decision: Both #9 and #10 are dependent.

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Now, compiling answers:

1) Independent
2) Independent
3) Dependent
4) Independent
5) Independent
6) Dependent
7) Dependent
8) Dependent
9) Dependent
10) Dependent

Double-checking #8: “putting it into the eraser” — this is odd phrasing. In real life, you wouldn’t put a pencil *into* an eraser. It might mean “putting it aside” or “using it up”. Either way, it’s removed from the pool → affects next draw → dependent. Correct.

Also, #5: spinning twice — even if you get even first, the spinner hasn’t changed → independent. Correct.

All good.

Final Answer:
1) Independent
2) Independent
3) Dependent
4) Independent
5) Independent
6) Dependent
7) Dependent
8) Dependent
9) Dependent
10) Dependent