QuestionWhich of the following pairs of events are independent? Select all correct answers.
Select all that apply:
You roll a die twice. Event $A$ is getting an even number on the first roll. Event $B$ is getting a 4 on the second roll.
You roll a die twice. Event $A$ is getting a 6 on the first roll. Event $B$ is getting a total of more than 7 .
You flip a coin and roll a die. Event $A$ is getting heads on the coin. Event $B$ is getting a 3 or more on the die.
You roll a die and flip a coin. Event $A$ is getting heads with the coin and getting 5 on the die. Event $B$ is getting 3 or more on the die.

Studdy Solution
Consider the fourth pair of events:
- Event $A$: Getting heads with the coin and getting 5 on the die. - Event $B$: Getting 3 or more on the die.
The occurrence of Event $A$ (getting a 5 on the die) affects the probability of Event $B$ (getting 3 or more on the die). Therefore, these events are not independent.
The independent pairs of events are:
1. You roll a die twice. Event $A$ is getting an even number on the first roll. Event $B$ is getting a 4 on the second roll.
2. You flip a coin and roll a die. Event $A$ is getting heads on the coin. Event $B$ is getting a 3 or more on the die.