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More ways to get Braingle...

Kick-off

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 

Puzzle ID:#11311
Fun:*** (2.39)
Difficulty:*** (2.46)
Category:Probability
Submitted By:jimbo*au******
Corrected By:Anupriya9

 

 

 



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?



Answer

Unco kicks: probability of a miss = 0.5
Jimbo 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.

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