Question

An even numbered card is chosen randomly from a set of cards labeled with the numbers 1 through 8. A second even numbered card is chosen after the first card is replaced. Are these dependent or independent events?
a.
dependent
b.
independent

Answer 1

Answer:

independent. This is a fun question. I never thought about how I would explain it before.

Explanation:

Can you think of anything that might influence the second even card being drawn?

• Let's make the question a whole lot easier. Suppose you have a coin and it's a fair one just coming from the mint. Suppose you toss it and you get either heads or tails.
• Can you think of a reason why you should get the same thing again or put another way, can you guess what you are going to get next?
• If you can't then the tosses are independent of each other. You haven't replaced anything, like once you get a tails, you weight the coin so you can never get tails again. That would be a dependent event.
• If you can guess consistently, you better submit a written paper to a math journal.

Now go back your your question. You replaced the card. The odds are the same as for the first toss. Is there anything that has changed your mind about being able to guess.

You can't guess, so the events are independent.