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:

Step1: Identify Four - Wheeled Vehicles (Event A)

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

Step2: Identify Vehicles in Event B (Pickup Truck or Motorcycle)

Vehicles in event B: pickup trucks (a type of truck) and motorcycles. Motorcycles are two - wheeled, so they are only in B (not in A). Pickup trucks are four - wheeled, so they are in the intersection of A and B.

Step3: Classify Each Vehicle

• Trucks (including pickup trucks): Four - wheeled and in B (since pickup truck is part of B), so in \(A\cap B\).
• Sedans: Four - wheeled, not in B (not a pickup truck or motorcycle), so only in A.
• Minivans: Four - wheeled, not in B, so only in A.
• SUVs: Four - wheeled, not in B, so only in A.
• Four - wheeler ATV: Four - wheeled, not in B, so only in A.
• Motorcycles: Not four - wheeled, in B, so only in B.

Answer:

• Only in \(A\) (not in \(B\)): sedans, minivans, SUVs, four - wheeler ATV.
• In \(A\cap B\): trucks (including pickup trucks).
• Only in \(B\) (not in \(A\)): motorcycles.

(Note: Since the actual Venn diagram dots are to be moved, the above is the classification of each vehicle type to their respective regions. If the Venn diagram has two circles, one for \(A\) and one for \(B\), the dots for sedans, minivans, SUVs, four - wheeler ATV go in the part of \(A\) not overlapping with \(B\); dots for trucks go in the overlapping part (\(A\cap B\)); dots for motorcycles go in the part of \(B\) not overlapping with \(A\).)