practice calculating probabilities using the addition and multiplication rules. which events are…

practice calculating probabilities using the addition and 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 bulls - eye.

practice calculating probabilities using the addition and 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 bulls - eye.

Answer

Explanation:

Step1: Recall definition of independent events

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

Step2: Analyze first option

Sarah picks a number less than 5 and keeps it. Then the sample - space for the second pick changes, so the events are dependent.

Step3: Analyze second option

Rolling a number cube and spinning a spinner are two separate actions. The result of rolling the number cube does not affect the result of spinning the spinner. So these events are independent.

Step4: Analyze third option

Eliza replaces the jack before choosing the second card. So the probability of choosing a black card on the second pick is not affected by choosing a jack on the first pick. These events are independent.

Step5: Analyze fourth option

Hayden puts on the first pair of socks, so the number of socks in the drawer changes for the second pick. The events are dependent.

Step6: Analyze fifth option

Choosing a card from a deck and throwing a dart are two unrelated actions. The result of choosing a card does not affect the result of throwing a dart. So these events are independent.

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.