independent and dependent event

check if my answers are right

1. tossing a coin twice- independent

2. pulling 2 socks from a drawer at the same time- dependent

3. drawing 2 marbles out of a bag- dependent

4. spinning a spinner 5 times- independent

5. spinning 2 different spinners 2 times- independent

6. drawing names out of hat-independent

7. throwing a pair of number cubes ten times- dependent

8. throwing one number 5 times- dependent

9. picking cards from deck-dependent

10. throwing 3 coins 3 times- independent

1. tossing a coin twice- independent (Correct)

2. pulling 2 socks from a drawer at the same time- dependent (Correct)

3. drawing 2 marbles out of a bag- dependent (Correct if you do not replace the first marble before drawing the second one)

4. spinning a spinner 5 times- independent (Correct)

5. spinning 2 different spinners 2 times- independent (Correct)

6. drawing names out of a hat-independent (Correct if you replace the name before drawing the next one, otherwise dependent)

7. throwing a pair of number cubes ten times- dependent (Incorrect, should be independent)

8. throwing one number 5 times- dependent (Incorrect, should be independent)

9. picking cards from deck-dependent (Correct if you do not replace the card before picking the next one)

10. throwing 3 coins 3 times- independent (Correct)

1. Tossing a coin twice - Independent: Each toss of the coin does not affect the outcome of the other toss.

2. Pulling 2 socks from a drawer at the same time - Dependent: The probability of pulling the second sock depends on the outcome of pulling the first sock.

3. Drawing 2 marbles out of a bag - Dependent: The probability of drawing the second marble depends on the outcome of drawing the first marble.

4. Spinning a spinner 5 times - Independent: Each spin of the spinner does not affect the outcome of the other spins.

5. Spinning 2 different spinners 2 times - Independent: The outcome of one spinner does not affect the outcome of the other spinner.

6. Drawing names out of a hat - Independent: Each name drawn does not affect the outcome of the other draws.

7. Throwing a pair of number cubes ten times - Dependent: The probability of the second throw depends on the outcome of the first throw.

8. Throwing one number 5 times - Dependent: The probability of each subsequent throw depends on the outcome of the previous throws.

9. Picking cards from a deck - Dependent: The probability of picking the second card depends on the outcome of picking the first card.

10. Throwing 3 coins 3 times - Independent: Each throw of the coins does not affect the outcome of the other throws.

Your answers are mostly correct, but there are a few corrections needed:

1. Tossing a coin twice - independent: Correct. Each toss of the coin is not influenced by the other toss.

2. Pulling 2 socks from a drawer at the same time - dependent: Incorrect. If the socks are taken out from the drawer at the same time, they can still be independent events because the outcome of one does not impact the outcome of the other. So, this would be independent.

3. Drawing 2 marbles out of a bag - dependent: Incorrect. When drawing marbles from a bag without replacement, the outcome of the second draw is dependent on the outcome of the first draw since the second draw has fewer marbles available. So, this would be dependent.

4. Spinning a spinner 5 times - independent: Correct. Each spin of the spinner is independent, as the previous spins do not affect the outcome of subsequent spins.

5. Spinning 2 different spinners 2 times - independent: Correct. Each spin on different spinners is independent, as the outcome of one spinner does not influence the other spinner.

6. Drawing names out of a hat - independent: Correct. Unless specified otherwise, drawing names out of a hat is typically an independent event.

7. Throwing a pair of number cubes ten times - dependent: Incorrect. Each throw of the number cubes is independent, as the previous throws do not impact the outcome of subsequent throws.

8. Throwing one number 5 times - dependent: Incorrect. Each throw of the number is independent, as the previous throws do not affect the outcome of subsequent throws.

9. Picking cards from a deck - dependent: Correct. When picking cards from a deck without replacement, the outcome of the second pick is dependent on the outcome of the first pick because the second pick has fewer cards available.

10. Throwing 3 coins 3 times - independent: Correct. Each throw of the coins is independent, as the previous throws do not affect the outcome of subsequent throws.

Keep in mind that the independence or dependence of the events can vary based on the specific conditions and rules given for each situation.