SOLUTION: It is so long since I had my bike stolen that I am considering selling my bike lock for �50 and just leaving the bike unlocked. Police statistics suggest that, if a bike is left

Question 1098897: It is so long since I had my bike stolen that I am considering selling my bike lock for
�50 and just leaving the bike unlocked. Police statistics suggest that, if a bike is left
unlocked:
� There is a 50% chance that it will not be stolen
� There is a 40% chance that the wheel (worth �75) will be stolen
� There is a 10% chance that the entire bike (worth �250) will be stolen
I try to think about the decision in terms of probabilities:
(a) Define a random variable X to represent this situation (i.e. define a mapping
from events to values of X, with probabilities).
(b) Calculate the expected value of X.
(c) Thinking in purely economic terms, does it make sense to sell the bike lock?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
X---------------p(x) ---x*p(x)
+50----------0.50------+25
-75----------0.40=====-30
-250---------0.10=====-25
+25-55=-30, E(X)
Economically, it doesn't make sense, since the expected value is negative.

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