Question

question
a motor company is manufacturing trucks, sedans, minivans, suvs, four - wheeler atv, and motorcycles. the dots in the venn diagram below show the type of each vehicle. a vehicle is selected at random.

• let ( a ) be the event of selecting a four - wheeled vehicle.
• let ( b ) be the event of selecting a pickup truck or a motorcycle.

move the dots on the venn diagram to place the dots in the correct region.
provide your answer below:

Explanation:

Answer:

To solve this, we first identify the vehicles for each event:

Step 1: Define Event \( A \) (Four - wheeled vehicles)

Four - wheeled vehicles from the list are: trucks, sedans, minivans, SUVs, four - wheeler ATV. These should be placed in the region corresponding to \( A \) (either only \( A \) or the intersection of \( A \) and \( B \) if applicable).

Step 2: Define Event \( B \) (Pickup truck or motorcycle)

Pickup trucks are a type of truck (so they are in \( A \) as well, since trucks are four - wheeled) and motorcycles are two - wheeled (so they are only in \( B \), not in \( A \)). So:

• Only \( A \) (four - wheeled, not pickup truck or motorcycle): sedans, minivans, SUVs, four - wheeler ATV.
• Intersection of \( A \) and \( B \) (four - wheeled and pickup truck): pickup trucks (since pickup trucks are four - wheeled and part of event \( B \)).
• Only \( B \) (not four - wheeled, but pickup truck or motorcycle): motorcycles (since motorcycles are two - wheeled and part of event \( B \)).

We would then move the dots representing each vehicle to these regions:

• Dots for sedans, minivans, SUVs, four - wheeler ATV go to the region of \( A \) only.
• Dots for pickup trucks go to the intersection of \( A \) and \( B \).
• Dots for motorcycles go to the region of \( B \) only.

Since the actual Venn diagram dots are not shown here (just the description), the key is to classify each vehicle based on the above logic and place them in the correct Venn diagram regions (only \( A \), only \( B \), or \( A\cap B \)) as per the definitions of \( A \) and \( B \).