Independent VS Dependent Probability

Front

What is Independent Probability?

Back

Independent probability refers to the likelihood of an event occurring that is not affected by the occurrence of another event. For example, drawing a marble from a bag, replacing it, and then drawing again.

Tags

CCSS.HSS.CP.A.5

Front

What is Dependent Probability?

Back

Dependent probability refers to the likelihood of an event occurring that is affected by the occurrence of another event. For example, drawing a marble from a bag and not replacing it before drawing again.

Tags

CCSS.HSS.CP.A.5

Front

Example of Independent Events: Drawing Marbles

Back

If you draw a marble from a bag, replace it, and draw again, the events are independent.

Tags

CCSS.HSS.CP.A.5

Front

Example of Dependent Events: Drawing Cards

Back

If you draw a card from a deck and do not replace it before drawing another card, the events are dependent.

Tags

CCSS.HSS.CP.A.5

Front

What does 'Replacement' mean in probability?

Back

Replacement means putting an item back into the sample space after it has been drawn, which affects whether events are independent or dependent.

Tags

CCSS.HSS.CP.A.5

Front

How does replacement affect probability?

Back

If an item is replaced, the probabilities remain the same for each draw (independent). If not replaced, the probabilities change with each draw (dependent).

Tags

CCSS.HSS.CP.A.5

Front

What is the probability of drawing a yellow marble twice with replacement?

Back

If there are 5 yellow marbles in a bag of 11 total marbles, the probability of drawing a yellow marble twice with replacement is (5/11) * (5/11) = 25/121.

Front

What is the probability of drawing a red marble and then a blue marble without replacement?

Back

If there are 3 red and 2 blue marbles, the probability of drawing a red marble first and then a blue marble is (3/5) * (2/4) = 6/20 = 3/10.

Front

Define 'Sample Space' in probability.

Back

The sample space is the set of all possible outcomes of a probability experiment.

Front

What is an example of a sample space for drawing a marble from a bag?

Back

If a bag contains 5 yellow, 4 green, and 2 blue marbles, the sample space is {yellow, green, blue}.