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.



There would be three scenarios for the said portfolio

_ Scenario 1: Both Bonds default _

Expected Value= (40*0.20) = 8

_ Scenario 2: Neither of the two Bonds default _

Expected Value= (200*0.45) = 90

_ Scenario 3: Either of the two Bonds default but not both _

Expected Value= (120*0.35) = 42

Sum of these expected values would amount to 140.

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