Question

A fair twelve-sided die is rolled once. Let A be the event that the outcome is a multiple of 3 (i.e., 3, 6, 9 or 12). Let B be the event that the outcome is an even number i.e., 2, 4, 6, 8, 10, or 12 ) Which is the following is correct regarding the events A and B? Circle ALL that apply • The two events are disjoint / not disjoint • The two events are • The two events are complements / not complements independent / not independent

Answer 1

Event A represents rolling a multiple of 3, and Event B represents rolling an even number. The events are not disjoint or complements, and they are independent.

Step-by-step explanation:

Event A represents the outcome of rolling a multiple of 3, namely a 3, 6, 9, or 12. Event B represents the outcome of rolling an even number, namely 2, 4, 6, 8, 10, or 12.

The two events are not disjoint, as there are numbers (6 and 12) that satisfy both events. However, they are not complements either, as the complement of A would be the outcomes that are not multiples of 3 and the complement of B would be the outcomes that are not even numbers.

To determine whether the events are independent, we need to calculate the probabilities of A and B and the probability of both A and B occurring. The probability of A is 4/12 = 1/3, the probability of B is 6/12 = 1/2, and the probability of both A and B is the number of outcomes that satisfy both events (2 and 6) divided by the total number of outcomes (12), which is 2/12 = 1/6. Since P(A) * P(B) = (1/3) * (1/2) = 1/6, the events are independent.