The latest nationwide political poll indicates that for Americans who

danrussekme

danrussekme

Answered question

2021-11-15

According to the most recent national political poll, there is a 0.55 percent chance that a randomly chosen American is conservative, a 0.30 percent chance that they are liberal, and a 0.15 percent chance that they are middle-of-the-road. Assuming that these probabilities are accurate, answer the following questions pertaining to a randomly chosen group of 10 Americans. What is the probability that none are conservative?

Answer & Explanation

Ruth Phillips

Ruth Phillips

Beginner2021-11-16Added 18 answers

Step 1 
Given information- 
according to the most recent American survey- 
The probability that they are conservative =0.55 
The probability that they are liberal =0.30 
The probability that they are middle-of-the-road =0.15 
We have given a problem of binomial distribution. 
We need to calculate the likelihood that none are conservative.
So, 
Probability of success, p=0.55 
No. of trial, n=10 
Let, X= probability that they are conservative. 
Given is the probability that k trials will result in success.
P(X=k)=(nk)×pk×(1p)nk 
Step 2 
So, 
The probability that none are conservative. 
No. of success desire, k=0 
P(X=0)=(100)×0.550×(10.55)100 
P(X=0)=0.0034 
Therefore, there is a 0.0034 percent chance that none are conservative.

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