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.
Answer
A
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.
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.
D
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.
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.
Explanation
Events are independent when one event does not change the probability of the other. Rolling a number cube and spinning a spinner are separate actions, so B is independent. In C, the jack is replaced before the second card is chosen, leaving the deck unchanged; the events are independent. Choosing a card and throwing a dart are also separate, so E is independent. A and D involve keeping or removing the first item, which changes what can be chosen next.
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