LC: ASM Exam 3 Question 5

I have been struggling to understand the solution to this question, and I was hoping someone could provide some insight.



5.) For three lives with independent lifetimes, you are given:

• 


• 


• 
  
  Calculate

The solution uses the equation:





However, I'm not sure how this equation is arrived at.



I know that , so I tried to generalize this to consider life 1 as and life 2 as .



This leads to , which doesn't look much like the solution, and doesn't seem particularly easy to calculate given the final term.



Could anyone explain where the solution's equation comes from?



Thanks!

LC: ASM Exam 3 Question 5