## 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

Question

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?

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3 months 2022-02-12T04:59:19+00:00 1 Answer 0 views 0

P(1) = 1 – 8/27 = 19/27

The probability that at least one of them will be elected is 19/27

Step-by-step explanation:

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

P(1) = 1 – P(None) …..1

Let P(A), P(B) and P(C) represent the probability for each of the three candidates to be elected .

P(A) = P(B) = P(C) = 1/3

The probability for each of the three candidates not to be elected is

P(A)’ = P(B)’ = P(C)’ = 1 – 1/3 = 2/3

P(None) = P(A)’ × P(B)’ × P(C)’= 2/3 × 2/3 × 2/3 = 8/27

From equation 1. Substituting the value of P(None)

P(1) = 1 – 8/27 = 19/27

The probability that at least one of them will be elected is 19/27