Thor is in a duel with his evil brother Loki. They exchange blows, and the chanc
ID: 2935901 • Letter: T
Question
Thor is in a duel with his evil brother Loki. They exchange blows, and the chance that Thor lands a hit with his hammer Mjolnir is 1 3 while the chances that Loki hits Thor with his spear is independent with probability 1 5 . Suppose that the strikes are essentially simultaneous, and neither duelist can ‘get ahead’ on strike attempts. The winner is the first one to land a strike while not getting hit in return (if they both hit at the same time then they stop and neither wins the bout). Calculate the probability that Loki wins
Explanation / Answer
Probability that Loki wins = probability (Loki hits Thor with spear and Loki doesn’t get hit in return)
= probability ( Loki hits Thor with spear and Thor doesn’t land a hit on Loki with hammer)
= probability (Loki hits Thor) * probability ( Thor doesn’t land a hit on Loki)
= (1/5) * (1-1/3) = 2/15 = 0.1333
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