Educational worksheet comparing independent and dependent events with real-life scenarios.

To solve this problem, we need to determine if the events in each scenario are Independent or Dependent.

Here is the simple rule to remember:
* Independent: The first event does not change the chances for the second event. (Usually happens when you put something back, or the events don't affect each other).
* Dependent: The first event does change the chances for the second event. (Usually happens when you keep the item out, so there is one less left for next time).

Let's look at each circle on the worksheet:

1. Josh's Socks: Josh picks a sock, puts it back, and picks another. Because he put the first one back, the total number of socks stays the same. The first pick doesn't change the second pick.
* Answer: Independent

2. Lana's Dice: Lana rolls a coin and then rolls a die. Rolling a coin has nothing to do with rolling a die. One doesn't change the other.
* Answer: Independent

3. Gerry's Chips: Gerry picks a chip and eats it (keeps it). Then he picks another from the same box. Since he ate the first one, there are fewer chips left in the box. The first pick changes the second pick.
* Answer: Dependent

4. Kara's Cards: Kara draws a card and does not replace it. Then she draws another. Because she didn't put the first card back, there is one less card in the deck. The first draw changes the second draw.
* Answer: Dependent

5. Students' Names (Jar): Students pick names from a jar. The text says "Zack draws first and Serra draws." It implies they are picking distinct people. Usually, in these problems, unless it says "put back," picking a name removes it from the jar. If Zack picks a name, that name is gone for Serra.
* Answer: Dependent

6. Grant's Dart Board: Grant hits a part of the board. Then he hits it again. Where the dart lands the first time does not change where it will land the second time. The board doesn't shrink or change.
* Answer: Independent

7. Principal's Names: The principal draws a name and then draws the second name. This implies the first name is kept out (to be the winner/first choice). Therefore, the pool of names gets smaller for the second draw.
* Answer: Dependent

8. Mrs. Kraft's Days: Mrs. Kraft wants to know how many ways students can choose two days. Choosing Monday and Tuesday is just a combination. The act of choosing one day doesn't physically remove "Tuesday" from the week for the next choice in a way that changes probability—it's just listing pairs. However, looking at the context of "Independent vs Dependent events" in probability: Does choosing the first day affect the probability of the second? If she picks Monday, can she pick Monday again? The problem asks for "two different days". If she picks Monday first, she cannot pick Monday second. This makes them dependent choices because the first choice restricts the second choice.
* *Self-Correction/Refinement:* In many school contexts, simply listing combinations is treated differently than physical removal. But let's look closer. "Choose two different days." If I pick Monday first, my options for the second day are Tue-Sun. If I had picked Tuesday first, my options for the second day would be Mon, Wed-Sun. The available options change based on the first pick. Thus, Dependent.

9. Eli's Coins: Eli chooses a coin, records it, and puts it back. Then he chooses again. Because he put it back, the coins in the pocket are exactly the same for the second turn.
* Answer: Independent

10. Emma's Cards: Emma draws a card and chooses a 4. This phrasing is tricky. It says "On the first flip... Emma draws a card and chooses a 4." It seems to imply a single event or a specific condition. Let's re-read carefully: "On the first flip of the deck, Emma draws a card and chooses a 4." This sounds like one event. Wait, looking at the pattern, these are all two-step processes. Let's assume it means she draws a card, looks at it, and maybe the second part is missing or implied? Actually, looking at the text again: "On the first flip of the deck, Emma draws a card and chooses a 4." This might be a typo in the problem or I am misreading. Let's look at the last one.

11. Ms. Chase's Balls: Ms. Chase picks a ball, records the color, and returns it. Then she picks again. Since she returned the ball, the contents of the bag are unchanged.
* Answer: Independent

12. Students' Numbers: Students pick a number 1-10. They write it on paper. Then they pick again. It does not say they put the number back. In fact, you can't really "put back" a written number into a hat of numbered papers unless specified. However, usually, if you pick a number from a list, you can pick the same number again unless told otherwise. BUT, looking at the standard "pick a number" problems: If I pick '5', is '5' still available? Yes, numbers aren't physical objects being removed unless it's a raffle. However, often these worksheets treat "picking a number" as independent unless it's a "raffle" style draw. Let's look for clues. "Pick a number... write it down... pick again." There is no removal mechanism described. Therefore, the first pick doesn't stop the second pick from being any number.
* Answer: Independent

Let's re-evaluate #10 (Emma). "On the first flip of the deck, Emma draws a card and chooses a 4." This sentence is incomplete compared to the others. It likely meant "Emma draws a card, keeps it, and draws another." If she keeps it, it's Dependent. If the text is just describing one event, it's not a pair. Given the other problems, it's highly likely this is a "without replacement" scenario hidden in bad grammar. Let's assume Dependent as "draws a card" usually implies holding onto it in these contrast exercises, unlike the ones that explicitly say "returns it".

Let's double check #8 (Mrs. Kraft). "Choose two different days." If the question is just about counting possibilities (combinatorics), it's not strictly probability independence. But in the context of "Event A affects Event B": If Event A is "Pick Day 1", does it affect "Pick Day 2"? Yes, because Day 2 cannot be Day 1. So they are Dependent.

Let's double check #12 (Students' Numbers). "Pick a number... write it down... pick again." If I pick 7, can I pick 7 again? Yes. The first action doesn't restrict the second. So they are Independent.

Summary of Answers:

* Josh (Socks, with replacement): Independent
* Lana (Coin/Die): Independent
* Gerry (Chips, eating/keeping): Dependent
* Kara (Cards, no replace): Dependent
* Students (Names, Zack/Serra): Dependent (One name taken)
* Grant (Dart board): Independent
* Principal (Names, draw then draw): Dependent (First name removed)
* Mrs. Kraft (Days, different days): Dependent (Cannot pick same day twice)
* Eli (Coins, put back): Independent
* Emma (Cards): Dependent (Implies keeping the card, standard deck problem)
* Ms. Chase (Balls, returns it): Independent
* Students (Numbers, write down): Independent (Numbers can be repeated)

Final Answer:

Independent Events:
* Josh has a bag of assorted dirty socks...
* Lana flips a coin and rolls a die...
* Grant has a dart board...
* Eli chooses a coin... (puts it back)
* Ms. Chase reaches into a bag... (returns it)
* Students are asked to pick a number... (write it down, pick again)

Dependent Events:
* For a grocery store promotion... (Gerry eats the chip)
* Kara randomly selects a card... (does not replace it)
* Students are drawing random names... (Zack draws first, Serra draws)
* The principal draws out the name... (then draws the second name)
* Mrs. Kraft asks her students... (choose two *different* days)
* On the first flip of the deck, Emma draws a card... (implies keeping it/no replacement mentioned)