independent event & Mutually Exclusive

Independent events are two or more events where the occurrence of one event does not affect the occurrence of the other.

Mutually exclusive events are two or more events that cannot occur at the same time.

The probability of both A and B occurring is P(A) * P(B).

The complement of an event is the set of outcomes in the sample space that are not included in the event.

Yes, because replacing the card means the outcome of the first draw does not affect the second draw.

Yes, because the outcome of rolling the die does not affect the outcome of flipping the coin.

The probability is calculated based on the ratio of black kittens to the total number of kittens.

No, if two events are mutually exclusive, the occurrence of one event means the other cannot occur, which contradicts independence.

Flipping a coin and getting heads or tails; you cannot get both at the same time.

There are 5 even numbers (2, 4, 6, 8, 10) out of 10 total cards, so the probability is 5/10 or 1/2.