Country x is planning to attack country y, and country y is anticipating the attack.

Country x can either attack by land or by sea and country y can either prepare for a land defense or a sea defense.

Both countries must choose either an all land or all sea strategy, they may not divide their forces.

The following are the probabilities of a successful invasion according to both strategies used:

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      x attacks by     y defends by     prob. of success
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          sea             sea                 80%
          sea             land               100%
          land            land                60%
          land            sea                100% 
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1) What should the strategy of country x be, assuming the goal is to maximize the probability of a successful invasion? Assume the goal of country y to be to minimize the probability of a successful invasion.

2)What is the final probability of a successful invasion assuming both utilize an optimal strategy?