1. In the fictional story The Legend of Sleepy Hollow, the Headless Horseman chases Ichabod Crane...
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1. In the fictional story "The Legend of Sleepy Hollow", the Headless Horseman chases Ichabod Crane through the New England countryside. A video game based on this legend has Crane choosing his route randomly, with a probability of 0.15 that he stays on the road and 0.85 that he cuts through the forest. If he stays on the road, there is a 92% chance of the Horseman catching Ichabod. If he cuts through the forest, there is only a 63% chance of being caught. A What is the probability that Ichabod stays on the road and the Horseman does not catch him? B What is the probability that the Horseman catches Ichabod? C₁ Find the probability that the next game has Mr. Crane cut through the forest, given that the Horseman will indeed catch him. 1. In the fictional story "The Legend of Sleepy Hollow", the Headless Horseman chases Ichabod Crane through the New England countryside. A video game based on this legend has Crane choosing his route randomly, with a probability of 0.15 that he stays on the road and 0.85 that he cuts through the forest. If he stays on the road, there is a 92% chance of the Horseman catching Ichabod. If he cuts through the forest, there is only a 63% chance of being caught. A What is the probability that Ichabod stays on the road and the Horseman does not catch him? B What is the probability that the Horseman catches Ichabod? C₁ Find the probability that the next game has Mr. Crane cut through the forest, given that the Horseman will indeed catch him.
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