A poll released this week found that in a random sample of registered voters, 60
ID: 3041354 • Letter: A
Question
A poll released this week found that in a random sample of registered voters, 60% indicated that they think Mr. Gavin Newsom “will run” for the presidency, 30% sail he “will not run” and 10% had no opinion. When asked their opinions on whether or not he would be elected, 66% of those who said he “will run” thought he could be elected, 25% of those who thought he “will not run” thought he could be elected; whereas, 20% of those who had no opinion said that he could be elected.
a. What percentage of registered voters (in this sample) thought that he could be elected?
b. Given that a person thought that Mr. Newsom could be elected, what is the probability that this person said Mr. Newsom “will not run” for the presidency?
c. Compute all the posterior probabilities.
Explanation / Answer
a) P(he could be elected) = 0.6 * 0.66 + 0.3 * 0.25 + 0.1 * 0.2 = 0.491
The percentage of voters = 49.1%
b)P(will not run for presidency | he could be elected) = P( he could be elected | will not run for presidency) * P(will not run for presidency)/P(he could be elected)
= 0.25 * 0.3 / 0.491 = 0.15