Question

hana has a bag containing one red (r), one blue (b), and one yellow (y) tile. she draws two tiles out of the bag, one after the other. which explanation and tree diagram represent a pair of dependent of events? once a tile is chosen, it can be chosen again: once a tile is chosen, it cannot be chosen again: once a tile is chosen, it cannot be chosen again: once a tile is chosen, it can be chosen again:

Explanation:

Step1: Understand dependent events

Dependent events: The outcome of the first event affects the outcome of the second event. In tile - drawing, if a tile is not replaced (i.e., once a tile is chosen, it cannot be chosen again), the probability of the second - draw is affected by the first - draw.

Step2: Analyze the tree - diagram structure

For dependent events (no - replacement), in the tree - diagram:

• When the first tile is drawn (say \(R\)), the second - draw options should be the remaining two tiles (\(B\) and \(Y\)).
• When the first tile is \(B\), the second - draw options should be the remaining two tiles (\(R\) and \(Y\)).
• When the first tile is \(Y\), the second - draw options should be the remaining two tiles (\(R\) and \(B\)).

In the first and fourth options, since the tiles can be chosen again (replacement), the events are independent. In the second option, there is an incorrect repetition (e.g., \(B - B\) is not possible in a no - replacement two - draw from a set of three distinct tiles \(R\), \(B\), \(Y\)).

In the third option:

• If the first tile is \(R\), the second - draw options are \(B\) and \(Y\).
• If the first tile is \(B\), the second - draw options are \(R\) and \(Y\).
• If the first tile is \(Y\), the second - draw options are \(R\) and \(B\). And the explanation “Once a tile is chosen, it cannot be chosen again” is correct for dependent events.

Answer:

The third option (with the explanation “Once a tile is chosen, it cannot be chosen again” and the corresponding tree - diagram where each first - draw branch leads to two non - repeating second - draw branches) represents a pair of dependent events.