Question

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).

(a) find the probability that the person opposed the tax or is female.
\\(p(\text{opposed the tax or is female}) = 0.829\\)
(round to the nearest thousandth as needed.)

(b) find the probability that the person supports the tax or is male.
\\(p(\text{supports the tax or is male}) = \\)
(round to the nearest thousandth as needed.)

Explanation:

Identify the given values and target

Using the Two-Way Contingency Table Probability knowledge point

• Total number of adults: \(N = 1078\)
• Number of males: \(n(\text{Male}) = 505\)
• Number of females: \(n(\text{Female}) = 573\)
• Number of people who support the tax: \(n(\text{Support}) = 416\)
• Number of males who support the tax: \(n(\text{Support} \cap \text{Male}) = 171\)
• Target: \(P(\text{supports the tax or is male})\)

Apply the addition rule for probability

Using the Addition Rule for Probability knowledge point

$$ P(\text{Support} \cup \text{Male}) = P(\text{Support}) + P(\text{Male}) - P(\text{Support} \cap \text{Male}) $$

$$ P(\text{Support} \cup \text{Male}) = \frac{416}{1078} + \frac{505}{1078} - \frac{171}{1078} $$

Calculate the final probability

Using the Addition Rule for Probability knowledge point

$$ P(\text{Support} \cup \text{Male}) = \frac{416 + 505 - 171}{1078} = \frac{750}{1078} \approx 0.69573 $$

Rounding to the nearest thousandth gives \(0.696\).

Answer:

(b) Find the probability that the person supports the tax or is male.

P(supports the tax or is male) = <blank>0.696</blank>
(Round to the nearest thousandth as needed.)