Question 11 • Concepts in Probability and Statistics
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?
Answer
A
Once a tile is chosen, it can be chosen again: Image with description A tree diagram showing three draws from a bag. The first level branches into three options, R, B, and Y. From R, the second level branches into B and Y. From B, the second level branches into R and Y. From Y, the second level branches into R and B. Each second-level branch excludes the tile already drawn at the first level.
B
Once a tile is chosen, it cannot be chosen again: Image with description A tree diagram showing three draws from a bag. The first level branches into three options, R, B, and Y. From R, the second level branches into B and Y. From B, the second level branches into R and Y. From Y, the second level branches into R and B. Each second-level branch excludes the tile already drawn at the first level.
C
Once a tile is chosen, it cannot be chosen again: Image with description A tree diagram showing three draws from a bag. The first level branches into three options, R, B, and Y. From R, the second level branches into R, B and Y. From B, the second level branches into R, B and Y. From Y, the second level branches into R, B and Y.
D
Once a tile is chosen, it can be chosen again: Image with description A tree diagram showing three draws from a bag. The first level branches into three options, R, B, and Y. From R, the second level branches into R, B and Y. From B, the second level branches into R, B and Y. From Y, the second level branches into R, B and Y.
Explanation
The draws are dependent when the first draw changes what is available for the second draw. Because Hana draws without replacing the first tile, each second-draw branch must exclude the tile already drawn—for example, after drawing R, only B or Y can be drawn. Choice B states this and shows the matching tree diagram.
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