Independent and 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(s).

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(s).

Front

How do you determine if two events are independent?

Back

Two events A and B are independent if P(A and B) = P(A) * P(B).

Front

How do you determine if two events are dependent?

Back

Two events A and B are dependent if P(A and B) ≠ P(A) * P(B).

Front

What is the formula for finding the probability of independent events?

Back

P(A and B) = P(A) * P(B).

Front

What is the formula for finding the probability of dependent events?

Back

P(A and B) = P(A) * P(B|A), where P(B|A) is the probability of B given A has occurred.

Front

If the probability of event A is 0.5 and the probability of event B is 0.4, what is the probability of both events occurring if they are independent?

Back

P(A and B) = 0.5 * 0.4 = 0.2.

Front

If the probability of event A is 0.5 and the probability of event B given A is 0.3, what is the probability of both events occurring?

Back

P(A and B) = P(A) * P(B|A) = 0.5 * 0.3 = 0.15.

Front

What is the probability of drawing two cards from a deck without replacement? Are the events independent or dependent?

Back

The events are dependent. The probability changes after the first card is drawn.

Front

In a scenario where you roll a die and flip a coin, are these events independent or dependent?

Back

These events are independent because the outcome of one does not affect the other.