Independent & 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. For example, flipping a coin and rolling a die are independent events.

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. For example, drawing two cards from a deck without replacement is a dependent event.

Front

What is the probability of an event?

Back

The probability of an event is a measure of the likelihood that the event will occur, expressed as a number between 0 and 1.

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, 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 drawing a card from a deck?

Back

The probability of drawing a specific card from a standard deck of 52 cards is 1/52.

Front

If a card is drawn and replaced, what type of event is this?

Back

This is an independent event because the replacement means the total number of cards remains the same for each draw.

Front

If a card is drawn and not replaced, what type of event is this?

Back

This is a dependent event because the total number of cards decreases with each draw, affecting the probabilities.

Front

What is the probability of drawing an even number from a set of cards numbered 1-10?

Back

There are 5 even numbers (2, 4, 6, 8, 10) out of 10 total cards, so the probability is 5/10 or 1/2.

Front

What is the probability of drawing a red marble from a bag containing 3 red, 4 gray, 6 white, and 5 black marbles?

Back

The probability of drawing a red marble is 3/(3+4+6+5) = 3/18 = 1/6.