suppose you roll to standard number cubes. let event a be rolling a 4 on the first die and let event b be rolling a 3 on the second die. are a and b independent events? are a and b mutually exclusive events. explain.

The events are independent and are not mutually exclusive.

Step-by-step explanation:

Two events A and B are independent if the outcome of each of them does not affect the outcome of the other.

And two events are mutually exclusive if these can't occur at the same time.

Here the events are:

a = rolling a 4 on the first die

b = rolling a 3 on the second die.

Becuase, these are number cubes, we know that the outcome of one die has no impact in the outcome of the other die.

And because each outcome is on a different die, we can conclude that these events are independent.

(rolling a 4 in the first die does not change the probability of getting a 3 when we roll the second die).

Now, the events are mutually exclusive?

No, we can roll both dices and get a 3 in the first one and a 4 in the second one, so these events can happen in the same time.