# Probability problem

Hello I need help to solve the task

At the start of the year a bond portfolio consists of 2 bonds each worth $100.At the end of the year if a bond defaults it will be worth $20.If it does not default the bond will be worth $100. The probability that both bond default is 20%.The probability that neither bond defaults is 45%. What is the mean of the year end portfolio value??

I know the answer is $140 but i don`t know how to calculate. Please help and explain.

Regards

dymny

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There would be three scenarios for the said portfolioScenario 1: Both Bonds defaultExpected Value= (40*0.20) = 8

Scenario 2: Neither of the two Bonds defaultExpected Value= (200*0.45) = 90

Scenario 3: Either of the two Bonds default but not bothExpected Value= (120*0.35) = 42

Sum of these expected values would amount to 140.

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Where is 120 from?

When either of two bonds default it means that only one of them defaults.

ie.

Total Value of Portfolio = Value of Non Defaulted Bond + Value of Defaulted Bond=100+20 =120