Kick-offProbability puzzles require you to weigh all the possibilities and pick the most likely outcome.
Jimbo is an ace goal kicker. On the average, he will kick a goal on 2 out of 3 occasions. Unco on the other hand, will normally only kick a goal on 1 out of 2 occasions.
Now Jimbo, being quick to spot an opportunity, challenges Unco to a kicking duel. They will each in turn take one kick for goal until a goal is scored. The winner will be the first to score a goal. "I'll even give you the first kick", says Jimbo generously to Unco. What is the probability that Jimbo wins the kicking duel? AnswerUnco kicks: probability of a miss = 0.5Jimbo kicks: probability of a win = 0.5 x 2/3 = 1/3 {Note Unco must have missed in order for Jimbo to get a kick at all} Unco kicks: probability of a second miss = 0.5x1/3x 0.5 = 1/12 {Note both Unco and Jimbo must have missed for Unco to get a second kick} Jimbo kicks: probability of goal = 1/12 x 2/3 = 1/18 Probability that Jimbo wins on first or second or third etc is: P = 1/3 + 1/18 + 1/108 + ...... Which is a geometric series with limiting sum = 2/5 Answer: Probability that Jimbo wins = 2/5. Hide What Next?
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