Independent vs 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 a card from a deck and then drawing another card without replacement.

Front

If two events A and B are independent, how do you find the probability of both occurring?

Back

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

Front

If two events A and B are dependent, how do you find the probability of both occurring?

Back

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 red marble and then a blue marble without replacement if there are 3 red and 2 blue marbles?

Back

P(red then blue) = (3/5) * (2/4) = 3/10.

Front

What is the probability of landing on red twice in a row with a spinner divided into 4 equal sections?

Back

P(red twice) = (1/4) * (1/4) = 1/16.

Front

What is the probability of drawing a heart first and then a spade from a standard deck of cards without replacement?

Back

P(heart then spade) = (13/52) * (13/51) = 1/16.

Front

How do you calculate the probability of selecting a purple chip followed by a black chip from a jar containing 4 white, 5 purple, and 1 black chip?

Back

P(purple then black) = (5/10) * (1/9) = 5/90 = 1/18.

Front

What is the probability of getting exactly two heads when flipping a coin three times?

Back

P(exactly 2 heads) = 3/8.

Front

What is the total number of outcomes when flipping a coin three times?

Back

Total outcomes = 2^3 = 8.