Question

multiplication rules. 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 bull’s - eye.

Explanation:

• First event: Sarah keeps the first number, so the second pick's probability is affected (dependent).
• Second event: Rolling a cube and spinning a spinner are independent actions (outcomes don't affect each other).
• Third event: Eliza replaces the card, so the deck remains the same (independent events).
• Fourth event: Hayden removes a pair, so the second pick's probability is affected (dependent).
• Fifth event: Choosing a card and throwing a dart are independent actions (outcomes don't affect each other).

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.