Independent & Dependent Events

Front

What are independent events in probability?

Back

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

Front

What are dependent events in probability?

Back

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

Front

How do you calculate the probability of independent events occurring together?

Back

To find the probability of two independent events A and B occurring together, multiply their individual probabilities: P(A and B) = P(A) * P(B).

Front

How do you calculate the probability of dependent events occurring together?

Back

To find the probability of two dependent events A and B occurring together, multiply the probability of the first event by the conditional probability of the second event: P(A and B) = P(A) * P(B|A).

Front

What is the probability of drawing a red marble from a bag containing 6 red and 5 green marbles?

Back

The probability of drawing a red marble is P(Red) = Number of Red Marbles / Total Marbles = 6 / (6 + 5) = 6/11.

Front

If Joe picks 2 marbles one after the other without replacement, what is the probability that both are red?

Back

The probability is P(Red1) * P(Red2|Red1) = (6/15) * (5/14) = 30/210 = 1/7.

Front

What is the probability of rolling an even number on a die?

Back

The probability of rolling an even number (2, 4, or 6) is P(Even) = 3/6 = 1/2.

Front

What is the probability of rolling an odd number on a die?

Back

The probability of rolling an odd number (1, 3, or 5) is P(Odd) = 3/6 = 1/2.

Front

If two pencils are picked from a basket of 5 purple and 9 brown pencils without replacement, what is the probability that both are purple?

Back

The probability is P(Purple1) * P(Purple2|Purple1) = (5/14) * (4/13) = 20/182 = 10/91.

Front

What is the difference between independent and dependent events?

Back

Independent events do not influence each other, while dependent events do influence each other.