In the game of Hearthstone, there is a card (Flamewaker) which, when triggered,

Question

In the game of Hearthstone, there is a card (Flamewaker) which, when triggered, will launch 2 bombs, one at a time. Each bomb chooses an enemy uniformly at random, and decreases its Hit Points by 1. If an enemy's Hit Points reach 0, it is destroyed, and future bombs will not target it. Clarification: The bombs might all hit the same enemy, or split amongst two enemies. If an enemy is destroyed from the first bomb, the second bomb will choose an enemy uniformly at random amongst the remaining enemies. Suppose there are three enemies, enemy A with 4 Hit Points, enemy B with 8 Hit Points and enemy C with 80 Hit Points. Suppose you play a card (Fireball) which first reduces enemy B's Hit Points by 6, and then triggers Flamewaker. What is the probability enemy B is destroyed? Suppose instead you play a card (Frostbolt) which first reduces enemy A's Hit points by 3. and then triggers Flamewaker. What is the probability enemy A is destroyed? Suppose you first play Frostbolt (against enemy A. which then triggers Flamewaker) and then play Fireball (against enemy B. which triggers Flamewaker again). What is the probability both enemy A and B are destroyed? Suppose you first play Fireball and then Frostbolt. What is the probability both enemy A and B are destroyed?

Explanation / Answer

Probability that a bomb will hit either A, B or with probability 1/3.

a. After Fireball is played, enemy B is left with 2 Hit Points. Thus, to destroy B, both the bombs should hit enemy B. Thus, the required probability is 1/3 x 1/3 = 1/9.

b. After Frostball is played, enemy A is left with 1 Hit Points. Thus, to destroy A, either of the bombs should hit enemy A. Thus, the required probability is 1/3 + 1/3 = 2/3.

c. After Frostball is played, enemy A is left with 1 Hit Points. After Fireball is played, enemy B is left with 2 Hit Points. A is destroyed with probability 2/3 and B is destroyed with probability 1/9. Therefore, probability both enemy A and B are destroyed is 2/3 x 1/9 = 2/27.

d. After Fireball is played, enemy B is left with 2 Hit Points. After Frostball is played, enemy A is left with 1 Hit Points. A is destroyed with probability 2/3 and B is destroyed with probability 1/9. Therefore, probability both enemy A and B are destroyed is 2/3 x 1/9 = 2/27.

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