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

Question

Question 4 options:

Drawing a ticket out of a jar, not replacing it, and drawing another ticket

Pulling a solid tie out of a drawer without replacing it, and then pulling another solid tie out of the drawer

Spinning a spinner, and then rolling a die

Studying every night and getting all A's

Answer 1

To determine whether the events described in the options are independent, we need to understand the concept of independent events. Two events are considered independent if the outcome of one event does not affect the outcome of the other event.

1. Drawing a ticket out of a jar, not replacing it, and drawing another ticket: These events are not independent. The outcome of the second draw is affected by the first draw because the total number of tickets in the jar is reduced.

2. Pulling a solid tie out of a drawer without replacing it, and then pulling another solid tie out of the drawer: These events are also not independent for the same reason as above. The second pull is affected by the first because the number of ties in the drawer changes after the first pull.

3. Spinning a spinner, and then rolling a die: These events are independent. The outcome of spinning the spinner does not affect the outcome of rolling the die.

4. Studying every night and getting all A's: These events are not independent. The act of studying influences the likelihood of getting A's, making them dependent events.

Conclusion: The only set of events that are considered independent is "Spinning a spinner, and then rolling a die."