Question

1. Which of the following is an example of independent events?

A. rolling a number cube and flipping a coin
B. drawing marbles from a bag without replacement after each draw
C. choosing members of a team from a group of 10 kids

2. Which of the following is an example of independent events?
A. selecting letter tiles from a bag without replacement
B. flipping a coin three times in a row
C. selecting one piece of fruit from a bag and eating it and then selecting another piece of fruit

3. Which of the following is an example of independent events?
A. selecting a coin from your pocket and spending it and then selecting another coin
B. a teacher selecting students' names from a hat without replacement
C. selecting letter tiles from a bag with replacement

Thank you!

Answer 1

1-B 2-A 3-B

Step-by-step explanation:

Answer 2

1: Rolling a number cube and flipping a coin are independent events. (Option A)

2: Selecting one piece of fruit from a bag and eating it and then selecting another piece of fruit are independent events. (Option C)

3: A teacher selecting students' names from a hat without replacement are independent events. (Option B)

Step-by-step explanation:

Independent events are those where the occurrence of one event does not affect the probability of the other event occurring. In other words, knowing the outcome of one event doesn't give you any additional information about the outcome of the other.

Justification for choices:

1: Rolling a number cube and flipping a coin are independent events because the outcome of one has no bearing on the outcome of the other. Each roll and flip has its own probability independent of the other. Option A is answer.

2: While selecting fruits without replacement might seem dependent, the chosen and remaining fruits are still distinct objects. The probability of picking a specific fruit doesn't change after consuming another fruit. Option C is answer.

3: Selecting names from a hat without replacement are independent events because even though the pool of names shrinks after each selection, the remaining names are still equally likely to be chosen. The probability of each name being picked remains independent of the previous selections. Option B is answer.

Note: Choices with replacement (like selecting letter tiles with replacement) are not independent because the remaining objects change and influence the probability of future selections.