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 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

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

Back

This is an independent event because replacing the card means the outcome of the first draw does not affect the second draw.

Front

What is the formula for calculating the probability of independent events occurring together?

Back

The probability of independent events A and B occurring together is P(A) * P(B).

Front

What is the formula for calculating the probability of dependent events?

Back

The probability of dependent events A and B occurring together is 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 rolling an odd number on a number cube?

Back

There are 3 odd numbers (1, 3, 5) out of 6 total numbers, so the probability is 3/6 or 1/2.

Front

What is the probability of rolling a number greater than 4 on a number cube?

Back

There are 2 numbers greater than 4 (5, 6) out of 6 total numbers, so the probability is 2/6 or 1/3.

Front

If two marbles are drawn from a bag without replacement, what type of event is this?

Back

This is a dependent event because the outcome of the first draw affects the outcome of the second draw.

Front

What is the probability of selecting a pen and then a pencil from a box containing 10 pens and 15 pencils?

Back

The probability is (10/25) * (15/24) = 1/4.