Question

Which of the following sets of events are considered independent events?

Question 4 options:

Selecting a red marble from a bag, and then tossing a coin


Drawing a ten from a deck of cards, not replacing the card, and then drawing another card


Pulling a brown sock out of a drawer without replacing it, and then pulling another brown sock out of the drawer


Earnings all A's, and getting into college

Answer 1

To determine whether the events are independent, we need to analyze whether the occurrence of one event affects the occurrence of another event.

1. **Selecting a red marble from a bag, and then tossing a coin**: These events are independent. The outcome of selecting a marble does not affect the outcome of tossing a coin.

2. **Drawing a ten from a deck of cards, not replacing the card, and then drawing another card**: These events are not independent. The first draw affects the probability of the second draw because the total number of cards and possibly the composition of the deck changes after the first draw.

3. **Pulling a brown sock out of a drawer without replacing it, and then pulling another brown sock out of the drawer**: These events are not independent. As in the previous case, pulling out one sock changes the number of socks available for the second event.

4. **Earnings all A's, and getting into college**: These events are likely dependent, as the performance in school can have an effect on college admissions, making it likely that earning all A's could positively influence the chances of getting into college.

Based on this analysis, the only independent events in the list are:

**Selecting a red marble from a bag, and then tossing a coin.**