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

which events are independent? check all that apply.\neach 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.\na number cube is rolled and a spinner is spun. henry rolls a multiple of 2 and lands on a red portion of the spinner.\ntwo cards are randomly chosen from a standard deck. eliza chooses a jack, replaces it, and then chooses a black card.\ntwo 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.\na 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.\neach 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.\na number cube is rolled and a spinner is spun. henry rolls a multiple of 2 and lands on a red portion of the spinner.\ntwo cards are randomly chosen from a standard deck. eliza chooses a jack, replaces it, and then chooses a black card.\ntwo 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.\na 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 the definition of independent events

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

Step2: Analyze the first - case

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

Step3: Analyze the second - case

Rolling a number cube and spinning a spinner are two separate actions. The outcome of rolling the number cube does not affect the outcome of spinning the spinner. So rolling a multiple of 2 on the number cube and landing on a red portion of the spinner are independent events.

Step4: Analyze the third - case

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). So these are independent events.

Step5: Analyze the fourth - case

Hayden chooses a black pair of socks and puts them on (does not replace them), then chooses another pair. The first pick affects the sample space for the second pick. So these are dependent events.

Step6: Analyze the fifth - case

Choosing a card from a standard deck and throwing a dart are two completely separate actions. The outcome of choosing a card does not affect the outcome of throwing a dart. So choosing an ace from a deck and hitting the bull's - eye with a dart are independent events.

Answer:

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.; 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.