Determine whether the events A and B are independent.
-A balanced die is rolled twice.
Event A: The sum of the two rolls is 8
Event B: The first roll comes up 3

Question

Determine whether the events A and B are independent.
-A balanced die is rolled twice. 
Event A: The sum of the two rolls is 8
Event B: The first roll comes up 3

Quizplus · Accepted Answer

The outcome of the first roll (event B) affects the probability of the sum of the two rolls being 8 (event A). For example, if the first roll is a 3, there are 5 outcomes for the second roll (2, 3, 4, 5, 6) that result in a sum of 8, out of 6 possible outcomes. If the first roll were different, the number of outcomes that could lead to a sum of 8 would also be different.

Determine Whether the Events a and B Are Independent