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). (a) find the probability that the person opposed the tax or is female. p(opposed the tax or is female)=0.83 (round to the nearest thousandth as needed.)

Explanation:

Step1: Identify relevant numbers

The number of people who oppose the tax is 613, the number of females is 558, and the number of females who oppose the tax is 291. The total number of people surveyed is 1053.

Step2: Use the formula for the union of two - events

The formula for $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Here, let $A$ be the event that a person opposes the tax and $B$ be the event that a person is female.
$P(A)=\frac{613}{1053}$, $P(B)=\frac{558}{1053}$, and $P(A\cap B)=\frac{291}{1053}$.
$P(A\cup B)=\frac{613 + 558-291}{1053}=\frac{880}{1053}\approx0.836$.

Answer:

0.836