Independent and mutually exclusive events

Front

What are independent events in probability?

Back

Independent events are events where the occurrence of one event does not affect the occurrence of another. For example, flipping a coin and rolling a die are independent events.

Front

What are mutually exclusive events?

Back

Mutually exclusive events are events that cannot occur at the same time. For example, when rolling a die, getting a 2 and getting a 5 are mutually exclusive events.

Front

If two events A and B are mutually exclusive, what can be said about their probabilities?

Back

If A and B are mutually exclusive, then P(A and B) = 0, meaning the probability of both events occurring together is zero.

Front

Can mutually exclusive events be independent?

Back

No, mutually exclusive events cannot be independent. If one event occurs, the other cannot occur, which means they are dependent.

Front

What is the probability of picking a spade or a diamond from a standard deck of cards?

Back

The probability of picking a spade or a diamond is the sum of their individual probabilities: P(spade) + P(diamond) = 1/4 + 1/4 = 1/2.

Front

When drawing cards with replacement, how are the events classified?

Back

The events are classified as independent because the outcome of the first draw does not affect the outcome of the second draw.

Front

What is an example of dependent events?

Back

An example of dependent events is drawing two cards from a deck without replacement. The outcome of the first draw affects the probabilities of the second draw.

Front

If A and B are independent events, what is the formula for their combined probability?

Back

The formula for the combined probability of independent events A and B is P(A and B) = P(A) * P(B).

Front

What does it mean if two events are dependent?

Back

Dependent events are events where the occurrence of one event affects the occurrence of another. For example, drawing two cards from a deck without replacement.

Front

Is it possible for two events to be neither independent nor mutually exclusive?

Back

Yes, two events can be dependent and not mutually exclusive, meaning they can occur together but the occurrence of one affects the probability of the other.