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
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) =
(round to the nearest thousandth as needed.)

Explanation:

Step1: Recall probability formula

The probability formula is $P(A)=\frac{n(A)}{n(S)}$, where $n(A)$ is the number of elements in event $A$ and $n(S)$ is the total number of elements in the sample - space. The total number of adults surveyed is $n(S)=1053$.

Step2: Calculate P(supports the tax or is male)

The number of people who support the tax is $406$. The number of males is $495$. The number of males who support the tax is $163$.
Using the formula $P(A\cup B)=P(A)+P(B)-P(A\cap B)$, where $A$ is the event of supporting the tax and $B$ is the event of being male.
$P(A)=\frac{406}{1053}$, $P(B)=\frac{495}{1053}$, and $P(A\cap B)=\frac{163}{1053}$.
$P(A\cup B)=\frac{406 + 495-163}{1053}=\frac{738}{1053}\approx0.691$.

Answer:

$0.691$