Problem

The table below shows the results of a survey that asked 1078 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).
$\begin{array}{rcccc} & \text { Support } & \text { Oppose } & \text { Unsure } & \text { Total } \\ \text { Males } & 162 & 325 & 15 & 502 \\ \text { Females } & 240 & 307 & 29 & 576 \\ \text { Total } & 402 & 632 & 44 & 1078\end{array}$
(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 thousand as needed.)
(b) Find the probability that the person supports the tax or is male.
$\mathrm{P}$ (supports the tax or is male) =
(Round to the nearest thousandth as needed.)

Answer

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Answer

Final Answer: The probability that the person supports the tax or is male is approximately \(\boxed{0.689}\).

Steps

Step 1 :Given the total number of people is 1078, the number of people who support the tax is 402, the number of males is 502, and the number of males who support the tax is 162.

Step 2 :Calculate the probability that a person supports the tax by dividing the number of people who support the tax by the total number of people. This gives \(\frac{402}{1078} \approx 0.373\).

Step 3 :Calculate the probability that a person is male by dividing the number of males by the total number of people. This gives \(\frac{502}{1078} \approx 0.466\).

Step 4 :Calculate the probability that a person is both male and supports the tax by dividing the number of males who support the tax by the total number of people. This gives \(\frac{162}{1078} \approx 0.150\).

Step 5 :Calculate the probability that the person supports the tax or is male by adding the probability that the person supports the tax and the probability that the person is male, and then subtracting the probability that the person is both male and supports the tax. This gives \(0.373 + 0.466 - 0.150 = 0.689\).

Step 6 :Final Answer: The probability that the person supports the tax or is male is approximately \(\boxed{0.689}\).

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