Answer:
The probability that the the person approves of the job the president is doing or is an independent is 0.47.
Step-by-step explanation:
The formula to compute the probability of event A or B is:
P (A ∪ B) = P (A) + P (B) - P (A ∩ B)
The data provided is shown in the table below.
The probability of a person approving the job the president is doing is:
[tex]P(A)=\frac{173}{402}= 0.43035[/tex]
The probability of a person belonging to the Independents is:
[tex]P(I)=\frac{21}{402}= 0.05224[/tex]
The probability of a person approving of the president and belonging to the Independents is:
[tex]P(A\cap I)=\frac{5}{402} =0.01244[/tex]
Compute the probability that the the person approves of the job the president is doing or is an independent as follows:
[tex]P(A\cup I)=P(A) + P(A)-P(A\cap I)\\=0.43035+0.05224-0.01244\\=0.47015\\\approx 0.47[/tex]
Thus, the probability that the the person approves of the job the president is doing or is an independent is 0.47.
