Roll a die.
Let A be the event that the outcome on the die is an even number.
Let B be the event that the outcome on the die is or smaller.
Let C be the event that the outcome on the die is or larger.
Choose the correct option(s)? [MSQ]
A and B are dependent events
A and B are independent events
B and C are dependent events
B and C are independent events
Solution
Option A: A and B are dependent events The event A (outcome is an even number) and event B (outcome is 3 or smaller) are independent because the outcome being an even number does not affect the probability of the outcome being 3 or smaller, and vice versa. So, option A is incorrect.
Option B: A and B are independent events As explained above, events A and B are independent. So, option B is correct.
Option C: B and C are dependent events The event B (outcome is 3 or smaller) and event C (outcome is 4 or larger) are dependent because if one event occurs, the other cannot. So, option C is correct.
Option D: B and C are independent events As explained above, events B and C are dependent. So, option D is incorrect.