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?

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