Independent and Dependent Events

Front

What are 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 are 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

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

Back

To find the probability of 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 dependent events A and B occurring together, use the formula: P(A and B) = P(A) * P(B|A), where P(B|A) is the probability of B given that A has occurred.

Front

What is the probability of drawing a specific color ball from a bag with replacement?

Back

The probability remains constant for each draw since the ball is replaced. It is calculated as the number of favorable outcomes divided by the total number of outcomes.

Front

What is the probability of drawing a specific color ball from a bag without replacement?

Back

The probability changes after each draw because the total number of balls decreases. It is calculated based on the remaining balls after each draw.

Front

In the context of probability, what does 'replacement' mean?

Back

Replacement means putting the item back into the sample space after it has been drawn, keeping the total number of items constant.

Front

What does 'without replacement' mean in probability?

Back

Without replacement means that once an item is drawn, it is not returned to the sample space, reducing the total number of items for subsequent draws.

Front

How do you determine if two events are independent or dependent?

Back

Two events are independent if the occurrence of one does not change the probability of the other. If the probability of one event changes based on the occurrence of the other, they are dependent.

Front

What is the formula for calculating the probability of drawing two specific items in succession with replacement?

Back

P(A and B) = P(A) * P(B), where both events are independent due to replacement.