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A car manufacturer is testing the ability of safety devices to limit damages in car accidents.

You are given:

• A test car has either front air bags or side air bags (but not both), each type being equally likely.
• The test car will be driven into either a wall or a lake, with each accident type being equally likely.
• The manufacturer randomly selects 1, 2, 3, or 4 crash test dummies to put into a car with front air bags.
• The manufacturer randomly selects 2 or 4 crash test dummies to put into a car with side air bags.
  
• Each crash test dummy in a wall-impact accident suffers damage randomly equal to 0.5 or 1, with damage to each dummy being independent of damage to the others.
• Each crash test dummy in a lake-impact accident suffers damage randomly equal to either 1 or 2, with damage to each dummy being independent of damage to the others.

One test car is selected at random, and a test accident produces total damage of 1.

Determine the expected value of the total damage for the next test accident, given that the kind of safety device (front or side air bags) and accident type (wall or lake) will remain the same.


On a 6 minutes par problème...