Possibly a Combination Problem

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SUMMARY

The optimal strategy for defeating three out of four dragons A, B, C, and D, with respective kill probabilities of 0.4, 0.6, 0.8, and 0.9, is to exclude dragon A from the fight. The remaining dragons B, C, and D should be fought in an order that maximizes the probability of success. The calculated probability of defeating dragons B, C, and D is 0.432, achieved by fighting them in any order. To ensure victory, it is essential to defeat the second and third dragons in the sequence.

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Jason76
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You have to kill three of four dragons A, B, C and D dragons in a row before you get to be with your true love (TL). The chances that you kill them are respectively 0.4, 0.6, 0.8 and 0.9. In what order should you fight them so as to maximize your chances of being with TL?

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Since you only need to kill three of the four dragons, the obvious strategy is to not fight the dragon where you only have a 0.4 chance of winning. The other three can be fought in any order giving you a (0.6)(0.8)(0.9)= 0.432 probability of winning.
 
To defeat 3 dragons in a row in 4 fights, we definitely need to defeat the 2nd and the 3rd. So we should pick the highest chances for those.
 

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