Two dice (one red and one green) are rolled, and the numbers that face up are observed. Test the pair of events for independence.
A: The red die is 1, 3, or 5; B: The green die is even.

A)A and B are independent
B) A and B are dependent

Question

Two dice (one red and one green) are rolled, and the numbers that face up are observed. Test the pair of events for independence. ​
A: The red die is 1, 3, or 5; B: The green die is even.
​
A)A and B are independent
B) A and B are dependent

Quizplus · Accepted Answer

The events A and B are independent because the outcome of one die does not affect the outcome of the other die. The probability of the red die being 1, 3, or 5 is 3/6 or 1/2, and the probability of the green die being even is also 3/6 or 1/2. Therefore, the probability of both events happening together is (1/2) * (1/2) = 1/4, which is equal to the probability of A and B happening separately. This satisfies the definition of independence.

Two Dice (One Red and One Green) Are Rolled, and the Numbers