Independent Vs Dependent Probability

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 event.

Front

What is the definition of dependent events in probability?

Back

Dependent events are two or more events where the occurrence of one event affects the occurrence of the other event.

Front

If two events are independent, how do you calculate the probability of both events occurring?

Back

For independent events A and B, the probability of both events occurring is P(A and B) = P(A) * P(B).

Front

If two events are dependent, how do you calculate the probability of both events occurring?

Back

For dependent events A and B, the probability of both events occurring is P(A and B) = P(A) * P(B|A), where P(B|A) is the probability of B occurring given that A has occurred.

Front

What is an example of independent events in a probability scenario?

Back

Flipping a coin and rolling a die are independent events because the outcome of one does not affect the outcome of the other.

Front

What is an example of dependent events in a probability scenario?

Back

Drawing two cards from a deck without replacement is an example of dependent events because the outcome of the first draw affects the second draw.

Front

In the context of drawing marbles, what does 'without replacement' mean?

Back

'Without replacement' means that once an item (like a marble) is drawn, it is not put back into the pool for the next draw, affecting the probabilities of subsequent draws.

Front

In the context of drawing marbles, what does 'with replacement' mean?

Back

'With replacement' means that after an item (like a marble) is drawn, it is put back into the pool for the next draw, keeping the probabilities the same for each draw.

Front

How does the concept of replacement affect the independence of events?

Back

If an event is conducted with replacement, the events are independent; if conducted without replacement, the events are dependent.

Front

What is the probability of drawing two white gumballs from a bag containing 3 white and 2 red gumballs without replacement?

Back

The probability of drawing two white gumballs without replacement is P(White1) * P(White2|White1) = (3/5) * (2/4) = 3/10.