Question

Determine which of the following pairs of events are independent.

a. Rolling a fair six-sided die and flipping a fair coin
b. Drawing two cards from a deck without replacement
c. Choosing a marble from a bag, replacing it, and choosing another
d. Selecting a red M&M from a bag and selecting another red M&M

Answer 1

a. Rolling a fair six-sided die and flipping a fair coin: Independent events. b. Drawing two cards from a deck without replacement: Dependent events. c. Choosing a marble from a bag, replacing it, and choosing another: Independent events with replacement. d. Selecting a red M&M from a bag and selecting another red M&M: Dependent events.

Step-by-step explanation:

1. a. Rolling a fair six-sided die and flipping a fair coin: These events are independent because the outcome of one does not affect the other. The outcome of rolling the die does not change the probability of flipping the coin.
2. b. Drawing two cards from a deck without replacement: These events are dependent because the deck changes after each draw, affecting the probabilities of the next draw.
3. c. Choosing a marble from a bag, replacing it, and choosing another: These events are independent when there is replacement, meaning the first pick does not affect the probabilities of the second pick.
4. d. Selecting a red M&M from a bag and selecting another red M&M: These events are dependent because the first selection affects the probability of selecting a second red M&M, assuming the M&M is not replaced.