Which set of events is dependent?(1 point)
Responses
choosing a marble from a box, replacing it, then choosing another marble
the event of getting two heads when flipping two fair coins
rolling a number cube and flipping a coin
choosing a ball from a bag and then choosing another ball without replacing the first
choosing a ball from a bag and then choosing another ball without replacing the first
The set of events that is dependent is: choosing a ball from a bag and then choosing another ball without replacing the first.
To determine which set of events is dependent, we need to understand what it means for events to be dependent. Events are dependent if the outcome of one event affects the outcome of another event.
Let's analyze each set of events:
1. Choosing a marble from a box, replacing it, then choosing another marble.
In this set of events, the marble is replaced before the second selection, meaning the outcome of the first event does not influence the outcome of the second event. Therefore, this set of events is independent.
2. The event of getting two heads when flipping two fair coins.
In this case, the outcome of the first coin flip does influence the outcome of the second coin flip. For example, if the first coin flip results in tails, it is impossible to get two heads. Therefore, this set of events is dependent.
3. Rolling a number cube and flipping a coin.
In this set of events, rolling a number cube and flipping a coin are independent events. The outcome of rolling the number cube does not affect the outcome of flipping the coin, and vice versa. Therefore, this set of events is independent.
4. Choosing a ball from a bag and then choosing another ball without replacing the first.
In this case, the outcome of the first selection affects the outcome of the second selection, since the ball is not replaced after the first selection. For example, if the first ball chosen is red, the probability of choosing another red ball on the second selection decreases. Therefore, this set of events is dependent.
Based on this analysis, the set of events that is dependent is: choosing a ball from a bag and then choosing another ball without replacing the first.