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

which events are independent? check all that apply.\n□ 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.\n□ 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.\n□ two cards are randomly chosen from a standard deck. eliza chooses a jack, replaces it, and then chooses a black card.\n□ 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.\n□ 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.\n□ 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.\n□ 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.\n□ two cards are randomly chosen from a standard deck. eliza chooses a jack, replaces it, and then chooses a black card.\n□ 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.\n□ 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

Brief Explanations:

Independent events are those where the outcome of one event does not affect the outcome of another.

  1. In the first case, since Sarah keeps the first - picked number, the sample space for the second pick is affected, so they are dependent.
  2. Rolling a number cube and spinning a spinner are separate actions with no influence on each other, so they are independent.
  3. Since Eliza replaces the first - chosen card, the probability of choosing the second card is not affected by the first choice, so they are independent.
  4. Hayden does not replace the first pair of socks, so the probability of choosing the second pair is affected by the first choice, making them dependent.
  5. Choosing a card from a deck and throwing a dart are two unrelated events with no impact on each other, so they are independent.

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.