Let event [tex]$A=$[/tex] The animal is a bird.
Let event [tex]$B=$[/tex] The animal can fly.
Which outcomes are in [tex]$A$[/tex] and [tex]$B$[/tex]?
| Animal | Is a bird | Can fly |
| :------- | :-------- | :-------- |
| Pig | | |
| Penguin | \checkmark | |
| Seagull | \checkmark | \checkmark |
| Tiger | | |
| Crow | \checkmark | \checkmark |
| Bat | | \checkmark |
| Mosquito | | \checkmark |
A. (penguin, seagull, crow)
B. (seagull, crow)
C. (penguin, seagull, crow, bat, mosquito)
D. (seagull, crow, bat, mosquito)
Answer (2)
Identify animals that are birds (event A ): Penguin, Seagull, Crow.
Identify animals that can fly (event B ): Seagull, Crow, Bat, Mosquito.
Find the intersection of A and B : Seagull, Crow.
The outcomes in A and B are: (seagull, crow) .
Explanation
Analyze the problem We are given a table with animals and their characteristics: whether they are birds and whether they can fly. Event A is defined as the animal being a bird, and event B is defined as the animal being able to fly. We need to find the animals that belong to both event A and event B , meaning they are both birds and can fly.
Identify animals in each event From the table, we can identify the animals that are birds (event A ) and the animals that can fly (event B ).
Animals that are birds (event A ): Penguin, Seagull, Crow. Animals that can fly (event B ): Seagull, Crow, Bat, Mosquito.
Find the intersection of the two events Now, we need to find the animals that are in both lists, i.e., the intersection of the two sets. These are the animals that are both birds and can fly.
Comparing the two lists, we find that the animals that are both birds and can fly are Seagull and Crow.
Determine the correct option Therefore, the outcomes that are in A and B are (seagull, crow). This corresponds to option B.
Examples
Understanding sets and their intersections is crucial in many real-world scenarios. For example, in marketing, you might want to target customers who are both interested in sports (event A) and live in a specific region (event B). The intersection of these two sets helps you focus your advertising efforts on the most relevant audience, maximizing the effectiveness of your campaign.
The animals that are both birds and can fly are the Seagull and the Crow. Therefore, the correct answer is option B: (seagull, crow).
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