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) $=$ (Round to the nearest thousandth as needed.)

Solution

Step 1 :The total number of adults surveyed is 1078.

Step 2 :The number of people who opposed the tax is 632.

Step 3 :The number of females is 576.

Step 4 :The number of females who opposed the tax is 307.

Step 5 :The probability of a person opposing the tax is calculated by dividing the number of people who opposed the tax by the total number of adults surveyed, which is \(\frac{632}{1078} \approx 0.586\).

Step 6 :The probability of a person being female is calculated by dividing the number of females by the total number of adults surveyed, which is \(\frac{576}{1078} \approx 0.534\).

Step 7 :The probability of a female opposing the tax is calculated by dividing the number of females who opposed the tax by the total number of adults surveyed, which is \(\frac{307}{1078} \approx 0.285\).

Step 8 :The probability of a person opposing the tax or being female is calculated by adding the probability of a person opposing the tax and the probability of a person being female, and then subtracting the probability of a female opposing the tax to avoid double counting, which is \(0.586 + 0.534 - 0.285 \approx 0.835\).

Step 9 :Final Answer: The probability that the person opposed the tax or is female is approximately \(\boxed{0.836}\).

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Source: https://solvelyapp.com/problems/17386/

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