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). $\begin{array}{rcccc} & \text { Support } & \text { Oppose } & \text { Unsure } & \text { Total } \\ \text { Males } & 162 & 325 & 15 & 502 \\ \text { Females } & 240 & 307 & 29 & 576 \\ \text { Total } & 402 & 632 & 44 & 1078\end{array}$ $P$ (opposed the tax or is female) $=0.836$ (Round to the nearest thousandth as needed.) (b) Find the probability that the persomsupports the tax or is male. $P$ (supports the tax or is male) $=0.689$ (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.)

Solution

Step 1 :Given the table of survey results, we are asked to find the probability that the person is not unsure or is female.

Step 2 :First, we calculate the total number of people surveyed, which is 1078.

Step 3 :Next, we find the number of females, which is 576, and the number of people who are not unsure, which is 1034 (the sum of those who support and those who oppose).

Step 4 :We also need to find the number of females who are not unsure, which is 547 (the sum of females who support and those who oppose).

Step 5 :We can now calculate the probabilities. The probability of a person being female is \(\frac{576}{1078} \approx 0.534\). The probability of a person not being unsure is \(\frac{1034}{1078} \approx 0.959\). The probability of a person being both female and not unsure is \(\frac{547}{1078} \approx 0.507\).

Step 6 :Finally, we calculate the probability of a person being not unsure or female. This is done by adding the probability of the person being female and the probability of the person not being unsure, and then subtracting the probability of the person being both female and not unsure (since we are double counting this scenario). So, the probability is \(0.534 + 0.959 - 0.507 \approx 0.986\).

Step 7 :Final Answer: The probability that the person is not unsure or is female is approximately \(\boxed{0.986}\).

From Solvely APP
Source: https://solvelyapp.com/problems/17393/

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