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?

Answer 1

Answer:

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