Math
Mike and Dave play a game in which each independently throws a dart at a target. Mike hits the target with probability 0.6, while Dave hits the target with probability 0.3. Mike wins the game if he hits the target and Dave misses. Dave wins the game if he hits the target and Mike misses. Otherwise the game is a tie. What is the probability that the game is a tie?
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The probability that the game is a tie is 0.42. This is because the probability of Mike hitting the target and Dave missing is 0.6 x 0.7 (1 - 0.3) = 0.42, and the probability of Dave hitting the target and Mike missing is 0.3 x 0.4 (1 - 0.6) = 0.42. Thus, the probability of either of these two scenarios occurring is 0.42 + 0.42 = 0.84, which is the probability that the game is a tie.