Feb 17 2009, 07:08 PM
Three clans of ninjas are meeting for a showdown. Ninja aren't a terribly loyal or honorable group and many belong to more than one clan.
47% are ninjas of the sword
53% are ninjas of the fist
45% are ninjas of the night
20% are both ninjas of the sword and ninjas of the fist
15% are both ninjas of the sword and ninjas of the night
13% are both ninjas of the fist and ninjas of the night
3% belong to all three clans
What is the probability that a ninja belongs to exactly one clan?
Feb 17 2009, 07:55 PM
If you assume that the ninjas belonging to two clans only belong to two clans and do not intersect with the 3% that belong to all 3 clans, draw out the Venn diagram.
Then P(sword only) = 0.47 - 0.20 - 0.03 - 0.15 = 0.09
P(fist only) = 0.53 - 0.20 - 0.03 - 0.13 = 0.17
P(night only) = 0.45 - 0.15 - 0.13 - 0.03 = 0.14
Add all 3 probabilities up = 0.09 + 0.17 + 0.14 = 0.40 = 40%
Feb 18 2009, 03:42 PM
Thanks a bunch gumdrop! You explained it very clearly.
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