Dependent and Independent Events Lesson Plans & Worksheets - Free Printable

Let’s go through each question one by one. We’re checking if two events are independent.

What does “independent” mean?

Two events are independent if the outcome of the first event does not affect the probability of the second event.

A simple way to check:
→ If you replace something (like putting a card back, or rolling again), it’s usually independent.
→ If you don’t replace (like taking a sock out and not putting it back), it’s usually not independent.

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1. You spin a spinner twice.

Each spin doesn’t change the spinner — so the result of the first spin doesn’t affect the second.

✔ Independent

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2. You choose a pair of shoes and a pair of socks.

Choosing shoes doesn’t change what socks are available — unless they’re tied together somehow (which they’re not). So these choices don’t affect each other.

✔ Independent

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3. You toss two different CDs.

Tossing one CD doesn’t change how the other lands. They’re separate objects.

✔ Independent

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4. You randomly select two cards from a standard deck of 52 cards without replacement.

“Without replacement” means after you pick the first card, you don’t put it back. So the second card is picked from only 51 cards — and the type of card you got first affects what’s left.

Example: If you pick an Ace first, there are fewer Aces left for the second pick.

✘ Not independent

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5. You roll a number cube once and flip the coin once.

Rolling a die has nothing to do with flipping a coin. One doesn’t change the other.

✔ Independent

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6. You get five cards in your starting hand in a game of poker.

In poker, you’re dealt 5 cards from one deck — no replacing. Each card you get changes what’s left for the next card.

So getting the first card affects the chances of getting the second, third, etc.

✘ Not independent

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7. You choose an outfit from a closet for yourself and a friend.

Assuming you have enough clothes and you’re choosing separately — your choice doesn’t limit your friend’s options (unless you’re sharing the same small closet and taking everything — but we assume normal situation).

✔ Independent

*(Note: If the problem meant you’re picking outfits from the same limited set without replacement, it might be dependent — but since it says “for yourself and a friend,” and doesn’t say you’re removing items permanently, we’ll assume independence.)*

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8. Are the following events independent? You roll a 3 and a 4.

This is vague — did you roll once or twice?

If you rolled once, you can’t get both a 3 and a 4 — so this isn’t even possible as two separate events.

But if you rolled twice, then yes — each roll is independent.

Since the question says “you roll a 3 and a 4”, it likely means two rolls.

✔ Independent *(assuming two separate rolls)*

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9. Which events are independent?

Let’s check each:

(A) You buy 2 different lottery tickets.
Buying one ticket doesn’t change the odds of the other — unless it’s the same drawing and you’re trying to win the same prize — but generally, each ticket is independent.

✔ Independent

(B) You draw 2 colored pens at the same time from a box that contains 20 red and green pens.
“At the same time” = without replacement. Drawing one pen changes what’s left for the second.

✘ Not independent

(C) You reach into a bag 20 times nightly, draw a gold marble, and return it to the bag.
You return it every time → so each draw is from the same full bag.

✔ Independent

(D) You draw a card and don’t replace it. Then you draw another card.
No replacement → second draw depends on first.

✘ Not independent

So independent events here: (A) and (C)

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10. Which events are independent?

(A) You draw 2 different raffle tickets.
If it’s from the same draw and you don’t replace, then not independent. But if it’s two separate draws with replacement, maybe. The wording is unclear.

But typically, “draw 2 different raffle tickets” implies without replacement → so ✘ Not independent.

Wait — let’s think: if you’re entering a raffle and buying two tickets, each ticket has its own chance — but if it’s one drawing and you hold two tickets, the events aren’t really sequential. This is tricky.

Actually, in most school problems, if you’re drawing two things without saying “with replacement”, it’s assumed without → so dependent.

But let’s look at others.

(B) You roll a die 15 times and do not get a 6.
Each roll is independent — whether you got a 6 before doesn’t change the next roll.

✔ Independent

(C) You draw a card and don’t replace it. Then you draw another card.
Same as #9(D) → ✘ Not independent

(D) You draw two marbles and get one black, one white.
Again, if drawn without replacement (which is usual), then the second draw depends on the first.

✘ Not independent

So only (B) is clearly independent.

Wait — what about (A)? Let’s reconsider.

If you buy two raffle tickets for the same drawing, the event “ticket 1 wins” and “ticket 2 wins” are mutually exclusive (only one winner?), so not independent. Or if multiple winners, still, holding two tickets changes your overall chance — but per ticket, maybe?

Actually, in probability terms, if the drawing is random and fair, the outcome of one ticket doesn’t affect another — but since they’re part of the same draw, technically, if one wins, the other can’t (if single winner). So they’re dependent.

To avoid confusion — in standard curriculum, unless specified “with replacement”, drawing multiple items is considered dependent.

So safest answer: Only (B) is independent.

But let’s double-check (A): “You draw 2 different raffle tickets.” If it’s like pulling two names from a hat without replacement — definitely dependent.

Yes — so only (B) is independent.

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Now let’s compile all answers clearly.

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Final Answer:

1. Yes
2. Yes
3. Yes
4. No
5. Yes
6. No
7. Yes
8. Yes (assuming two separate rolls)
9. A and C
10. B