Respuesta :
Answer: The probability that a randomly selected citizen has a favorable or unfavorable opinion is 1 or 100%.
In this question, we have only two answers favorable or unfavorable.
A person can't have both opinions at the same time.
So these events - favorable and unfavorable are mutually exclusive events i.e one event cannot occur when the other occurs.
Let P(F) be the probability of a person who has a favorable opinion
P(UF) be the probability of a person who has an unfavorable opinion
[tex]\boldsymbol{\mathbf{P(F) = \frac{Total people with favorable responses}{Total people in the survey}}}[/tex]
[tex]\boldsymbol{\mathbf{P(F) = \frac{62}{100}}}[/tex]
[tex]\boldsymbol{\mathbf{P(UF) = \frac{No. of people with unfavorable opinion}{Total number of people in the survey}}}[/tex]
[tex]\boldsymbol{\mathbf{P(UF) = \frac{38}{100}}}[/tex]
Now, the probability of either one of two mutually exclusive events occurring is:
[tex]\boldsymbol{\mathbf{P(F or UF) = P(F) + P(UF)}}[/tex]
[tex]\boldsymbol{\mathbf{P(F or UF) = \frac{62}{100} + \frac{38}{100} = \frac{100}{100}=1}}[/tex]
