independent event & Mutually Exclusive

Front

What is the definition of independent events in probability?

Back

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

Front

What is the definition of mutually exclusive events?

Back

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

Front

If two events A and B are independent, what is the probability of both A and B occurring?

Back

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

Front

What is the complement of an event?

Back

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

Front

In a probability experiment, if you draw a card from a deck and replace it, are the events independent?

Back

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

Front

If you roll a die and flip a coin, are these two events independent?

Back

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

Front

What is the probability of drawing a black kitten from a litter of kittens that includes both black and gray kittens?

Back

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

Front

Can two events be both independent and mutually exclusive?

Back

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

Front

What is an example of mutually exclusive events?

Back

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

Front

What is the probability of drawing an even number from a set of cards numbered 1-10?

Back

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