13.4 Independent vs Dependent

Front

What is an independent event in probability?

Back

An independent event is one where the outcome of one event does not affect the outcome of another event.

Front

What is a dependent event in probability?

Back

A dependent event is one where the outcome of one event affects the outcome of another event.

Front

If a marble is drawn from a bag and replaced, what type of event is this?

Back

This is an independent event because the replacement means the total number of marbles remains the same.

Front

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

Back

This is a dependent event because the total number of cards changes after the first draw.

Front

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

Back

The probability is 3/(3+4+6+5) = 3/18 = 1/6.

Front

What is the probability of drawing a gray marble after drawing a red marble and replacing it?

Back

The probability remains the same as the first draw: 4/(3+4+6+5) = 4/18 = 2/9.

Front

In a scenario where you draw a cube, replace it, and then draw again, what type of events are these?

Back

These are independent events.

Front

In a scenario where you draw a card, do not replace it, and then draw again, what type of events are these?

Back

These are dependent events.

Front

What is the probability of drawing a red cube, replacing it, and then drawing a white cube from a bag of 5 striped cubes, 3 dotted cubes, 4 white cubes, and 3 red cubes?

Back

The events are independent, and the probability is (3/15) * (4/15) = 12/225 = 4/75.

Front

What is the probability of spinning red on a spinner and picking a red marble from a bag of 2 red marbles, 3 green marbles, and 3 blue marbles?

Back

The events are independent, and the probability is (1/3) * (2/8) = 2/24 = 1/12.