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three candidates run for different offices in different cities. each has a one in three chance...

three candidates run for different offices in different cities. each has a one in three chance of being elected in his/her city. what is the probability that at least one of them will be elected
Math   Statistics-And-Probability   
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Answer #1

Suppose there are 3 candidates A,B and C running for election in 3 different cities.

Given that,

Probability that candidate A got elected in his/her city=Probability that candidate B got elected in his/her city=Probability that candidate C got elected in his/her city = 1/3

Therefore, probability that a candidate will not be elected is 1-1/3 = 2/3

Now the probability that at least one of them will be elected = 1- probability that none of them will be elected.

Probability that none of them will be elected=

Therefore, the probability that at least one of them will be elected

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