# Would an actuary for the company recommend that the cars be recalled in the following case:After 13,000 cars of a certain model are sold, it is discovered that about 0.04% of these cars contain a...

Would an actuary for the company recommend that the cars be recalled in the following case:

After 13,000 cars of a certain model are sold, it is discovered that about 0.04% of these cars contain a part that could lead to an accident. A recall would cost the company 18,000 $ per vehicle. An average car related lawsuit settles for 20,000,000. Because they want to maintain a positive public image, the company would do a recall of the cars unless it costs twice as much as paying for the lawsuits.

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### 1 Answer

After 13000 cars of a certain model are sold, it is discovered that about 0.04% of these cars contain a part that could lead to an accident. A recall would cost the company $18000 per vehicle.

The total cost associated with recalling the cars is $13000*18000 = $234*10^6

An average car related lawsuit would settle for $20000000 and there is a 0.04% probability of the company having to face a lawsuit for the 13000 cars sold. This gives the cost associated with the lawsuits as 0.04*13000*20000000/100 = $104*10^6

Two times the cost of paying for the lawsuits is $208*10^6 and the cost of recalling the cars is $234*10^6.

**As the cost of recalling the cars is more than twice the cost of paying for the lawsuits, the actuary would recommend not to recall the cars.**