Question

• A, the strongest, knocks out the opponent it attacks with probability 1/2

• B knocks out the opponent it attacks with probability 1/3

• C, the weakest, knocks out the opponent it attacks with probability 1/6,

The battle starts with all Pokemons present (thus, at the first round, A attacks B, while B and C attack A). When there is at most one Pokemon standing, rounds keep being counted, but no attack occurs. After the first round, what is the probability that all Pokemons {A,B,C} remain active? What is the probability that only {A,C}, or {B,C} or just C remain active.

Answer 1

1)what is the probability that all Pokemons {A,B,C} remain active

A attacks B = 1- 1/2 = 1/2

B attack A = 1 - 1/3 = 2/3

C attack A = 1 - 1/6 = 5/6

Total Probability = 1/2 * 2/3 * 5/6 = 0.278

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probability that only {A,C}, or {B,C} or just C remain active.

{A,C} = 1/2 * 2/3 * 5/6 =0.277777778

{B,C} = 1/2 * 1/3 *1/6 +1/2 * 1/3 *5/6 + 1/2 * 2/3 *1/6 =0.222222222

C = 1/2 * 1/3 *1/6 +1/2 * 1/3 *5/6 + 1/2 * 2/3 *1/6 =0.222222222

Total Probability = 0.722

Please revert in case of any doubt.

Please upvote. Thanks in advance