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?
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)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Question
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?
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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