Let’s go through each problem one by one. We need to decide if the events are
independent or
dependent.
Remember:
-
Independent events: The outcome of the first event does NOT affect the second event.
-
Dependent events: The outcome of the first event DOES affect the second event (like when you don’t replace something, so there’s less left).
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Problem 1:
> Kathy draws a 4 from a set of cards numbered 1-10 and rolls a 2 on a number cube.
Drawing a card and rolling a die are two separate things. What she gets on the card doesn’t change what happens with the die roll — they’re unrelated.
✔ So this is
independent.
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Problem 2:
> John chooses a book from the shelf to read, and then Brian chooses a different book from the remaining books.
John takes one book → now there’s one less book for Brian. That means Brian’s choice depends on what John took.
✔ So this is
dependent.
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Problem 3:
> Adrian chooses a baseball card from a stack and does not return it to the stack. Then Jenna chooses a card from stack.
Adrian removes a card and doesn’t put it back → so the total number of cards changes, and Jenna has fewer options. Her chance depends on what Adrian did.
✔ So this is
dependent.
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Problem 4:
> Mike draws a 7 from ten cards numbered 1 through 10. He replaces the card. Then Allison draws a 5.
Mike puts the card back → so the deck is still 10 cards when Allison picks. Her draw isn’t affected by Mike’s draw because everything was reset.
✔ So this is
independent.
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Final Answer:
1. independent
2. dependent
3. dependent
4. independent
Parent Tip: Review the logic above to help your child master the concept of independent events worksheet.
