Question

the table below shows the results of a survey that asked 1053 adults from a certain country if they favored or opposed a tax to fund education. a person is selected at random. complete parts (a) through (c).
males females total
support 163 243 406
oppose 322 291 613
unsure 10 24 34
total 495 558 1053
(a) find the probability that the person opposed the tax or is female. p(opposed the tax or is female) = 0.836 (round to the nearest thousandth as needed.)
(b) find the probability that the person supports the tax or is male. p(supports the tax or is male) = 0.701 (round to the nearest thousandth as needed.)
(c) find the probability that the person is not unsure or is female. p(is not unsure or is female) = (round to the nearest thousandth as needed.)

Explanation:

Step1: Find total number of non - unsure people

The total number of people is $n = 1053$, and the number of unsure people is $34$. So the number of non - unsure people is $1053 - 34=1019$. The total number of females is $558$.

Step2: Calculate the probability

The probability $P$ (is not unsure or is female) is given by the formula $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Here, event $A$ is "not unsure" and event $B$ is "female". The number of non - unsure females is $558 - 24=534$.
The probability of being not unsure $P(A)=\frac{1019}{1053}$, the probability of being female $P(B)=\frac{558}{1053}$, and the probability of being non - unsure and female $P(A\cap B)=\frac{534}{1053}$.
$P(A\cup B)=\frac{1019 + 558-534}{1053}=\frac{1043}{1053}\approx0.990$

Answer:

$0.990$