Sets and Venn Diagrams

Question 1 • TN-Algebra II B SC 26-27 (For Credit)

Which events are independent? Check all that apply.

Answer

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

Events are independent when the outcome of one does not change the probability of the other. In B and E, a roll and spinner spin, or a card draw and dart throw, are separate actions, so one result does not affect the other. In C, the jack is replaced before the second draw, restoring the deck and leaving the chance of a black card unchanged. A and D involve choosing without replacement, so the first choice changes what remains and affects the probability of the second choice.

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