In some city, 50% of the eligible voters prefer candidate A, 40% prefer candidate B, 10% have no preference. You randomly sample 12 eligible voters. What is the probability that all of them will prefer candidate A? Define a random variable X to be the number of candidate A Which values may have the random variable X?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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In some city, 50% of the eligible voters prefer candidate A, 40% prefer candidate B, 10% have no preference. You randomly sample 12 eligible voters.

  1. What is the probability that all of them will prefer candidate A?
  2. Define a random variable X to be the number of candidate A Which values may have the random variable X?
Expert Solution
Step 1

1.

It is given that, 50% of the eligible voters prefer candidate A and 12 eligible voters are selected.

Step 2

Here, the opinion for the choices of the voters are independent to each other. Hence, each of eligible voter has 0.50 chance to prefer candidate A.

Thus, the required probability is, 0.502 ≈ 0.000244.

Thus, the probability that all of them will prefer candidate A is 0.000244.

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