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 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, use: 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 formula for calculating the probability of selecting two items without replacement?

Back

The probability of selecting two items without replacement is calculated as: P(first item) * P(second item after first).

Front

If a bag contains 3 red balls and 2 blue balls, what is the probability of drawing a red ball first and then a blue ball without replacement?

Back

P(red first) = 3/5; P(blue second | red first) = 2/4. Therefore, P(red, blue) = (3/5) * (2/4) = 3/10.

Front

What is the total number of outcomes when rolling two dice?

Back

The total number of outcomes when rolling two dice is 6 (for the first die) * 6 (for the second die) = 36.

Front

What is the probability of drawing two apples from a bowl of 8 apples and 8 oranges without replacement?

Back

P(apple first) = 8/16; P(apple second | apple first) = 7/15. Therefore, P(apple, apple) = (8/16) * (7/15) = 7/30.

Front

In a jar with 4 white chips, 5 purple chips, and 1 black chip, what is the probability of drawing a purple chip followed by a black chip without replacement?

Back

P(purple first) = 5/10; P(black second | purple first) = 1/9. Therefore, P(purple, black) = (5/10) * (1/9) = 1/18.

Front

What is the probability of selecting a brown M&M from a bowl containing 4 yellow, 6 orange, 3 green, 5 blue, and 2 brown M&Ms?

Back

Total M&Ms = 20. P(brown) = 2/20 = 1/10.