which events are independent? check all that apply. each number 1 through 10 is written on a slip of paper…

which events are independent? check all that apply. each number 1 through 10 is written on a slip of paper, placed in a hat, and randomly picked. sarah picks a number less than 5, keeps it, and then picks an odd number. a number cube is rolled and a spinner is spun. henry rolls a multiple of 2 and lands on a red portion of the spinner. two cards are randomly chosen from a standard deck. eliza chooses a jack, replaces it, and then chooses a black card. two pairs of socks are randomly chosen from a drawer. hayden chooses a black pair of socks, puts them on, and then chooses another black pair. a card is randomly chosen from a standard deck and a dart is randomly thrown. olivia chooses an ace and the dart hits the bulls - eye.

which events are independent? check all that apply. each number 1 through 10 is written on a slip of paper, placed in a hat, and randomly picked. sarah picks a number less than 5, keeps it, and then picks an odd number. a number cube is rolled and a spinner is spun. henry rolls a multiple of 2 and lands on a red portion of the spinner. two cards are randomly chosen from a standard deck. eliza chooses a jack, replaces it, and then chooses a black card. two pairs of socks are randomly chosen from a drawer. hayden chooses a black pair of socks, puts them on, and then chooses another black pair. a card is randomly chosen from a standard deck and a dart is randomly thrown. olivia chooses an ace and the dart hits the bulls - eye.

Answer

Explanation:

Step1: Recall independent - event definition

Two events are independent if the occurrence of one event does not affect the probability of the occurrence of the other event.

Step2: Analyze each option

Option 1:

Sarah picks a number less than 5 and keeps it, then picks an odd - number. Since she keeps the first number, the sample space for the second pick is affected. So these are dependent events.

Option 2:

Rolling a number cube and spinning a spinner are two separate actions. The outcome of rolling a multiple of 2 on the number cube has no impact on the outcome of landing on a red portion of the spinner. These are independent events.

Option 3:

Eliza chooses a jack, replaces it, and then chooses a black card. Since the card is replaced, the probability of choosing a black card on the second draw is not affected by the first draw (choosing a jack). These are independent events.

Option 4:

Hayden chooses a black pair of socks, puts them on, and then chooses another black pair. Since the first pair is removed from the sample space, the probability of choosing the second pair is affected. These are dependent events.

Option 5:

Choosing a card from a standard deck and throwing a dart are two completely separate actions. The outcome of choosing an ace from the deck has no influence on the outcome of the dart - throw hitting the bull's - eye. These are independent events.

Answer:

B. A number cube is rolled and a spinner is spun. Henry rolls a multiple of 2 and lands on a red portion of the spinner. C. Two cards are randomly chosen from a standard deck. Eliza chooses a jack, replaces it, and then chooses a black card. E. A card is randomly chosen from a standard deck and a dart is randomly thrown. Olivia chooses an ace and the dart hits the bull's - eye.