Which set of events is dependent?
a choosing a marble from a box, replacing it, then choosing another marble
b choosing a ball from a bag and then choosing another ball without replacing the first
c the event of getting two heads when flipping two fair coins
d rolling a number cube and flipping a coin
a choosing a marble from a box, replacing it, then choosing another marble
The set of events that is dependent is option c: the event of getting two heads when flipping two fair coins.
To determine which set of events is dependent, we need to understand the concept of dependence in probability.
In probability, events are said to be dependent if the outcome of one event affects the outcome of another event. On the other hand, events are independent if the outcome of one event does not impact the outcome of another event.
Let's analyze each set of events in the given options:
a) Choosing a marble from a box, replacing it, then choosing another marble: This set of events is independent because replacing the marble ensures that the outcome of the first selection does not affect the second selection.
b) Choosing a ball from a bag and then choosing another ball without replacing the first: In this case, the events are dependent because the outcome of the first selection affects the number of balls of each type remaining in the bag, which consequently changes the probability of the outcomes for the second selection.
c) The event of getting two heads when flipping two fair coins: This is an independent event. When flipping a fair coin, the outcome of one flip does not impact the outcome of the other flip. So, each coin flip is independent, making this set of events independent.
d) Rolling a number cube and flipping a coin: Similar to the previous example, this set of events is also independent. Rolling a number cube and flipping a coin are separate actions, and the outcome of one action does not affect the outcome of the other.
Therefore, the set of events in option b, which involves choosing a ball from a bag and then choosing another ball without replacing the first, is the dependent set of events.