## Mathematics in the Financial Industry

"We use probability a lot when deciding whether or not to offer someone a loan. For example, say a family walks in here asking for $200,000 to buy a house. We run the credit check and find that there are three possible outcomes: a 5% chance we never see them again and lose the 200 grand, a 60% chance that they pay it back and we make $50,000 in interest, and a 35% chance that we have to foreclose on the house and get our money back but don't get any interest.

"You might think it's a bad idea to gamble $200,000 to make $50,000. But let's calculate the *expected value* of this transaction by multiplying the probability of each outcome by the amount of money we stand to gain or lose if it happens. 0.05 times negative $200,000 is negative $10,000, and 0.6 times positive $50,000 is positive $30,000. The benefit outweighs the risk, so it makes sense to give the family a loan.

"Does that make sense? Is any of this helping you study for your exam?"

You say yes, thank you and hurry out of the bank; it didn't seem like that bank manager liked you very much.

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