Question

a recent census found that 52.1% of adults are female, 10.8% are divorced, and 6.3% are divorced females. for an adult selected at random, let f be the event that the person is female, and d be the event that the person is divorced.
a. obtain p(f), p(d), and p(f&d).
b. determine p(f or d), and interpret your answer in terms of percentages.
c. find the probability that a randomly selected adult is male.
a. obtain p(f), p(d), and p(f&d).
p(f) = 0.521 (type an integer or a decimal. do not round.)
p(d) = 0.108 (type an integer or a decimal. do not round.)
p(f&d) = 0.063 (type an integer or a decimal. do not round.)
b. determine p(f or d), and interpret your answer in terms of percentages.
p(f or d) = 0.566 (type an integer or a decimal. do not round.)
interpret p(f or d) in terms of percentages. select the correct choice below and fill in the answer box within your choice.
(type an integer or a decimal. do not round.)
○ a. □% of adults are divorced females.
○ b. □% of divorced adults are female.
○ c. □% of adult females are divorced.
○ d. □% of adults are either female or divorced or both.

Explanation:

Step1: Recall the formula for \(P(F\ or\ D)\)

The formula for \(P(F\ or\ D)\) is \(P(F\cup D)=P(F)+P(D)-P(F\cap D)\).

Step2: Substitute the given values

We know \(P(F) = 0.521\), \(P(D)=0.108\), and \(P(F\cap D)=0.063\).
Substituting these values into the formula:
\(P(F\cup D)=0.521 + 0.108-0.063\)
\(P(F\cup D)=0.566\)

Step3: Interpret the result

The probability \(P(F\ or\ D)\) represents the probability that a randomly - selected adult is either female or divorced or both. In percentage terms, we multiply by \(100\). So \(0.566\times100 = 56.6\%\)

Step4: Find the probability that an adult is male

Since \(P(F)+P(M)=1\) (where \(M\) is the event that the person is male), and \(P(F) = 0.521\)
\(P(M)=1 - P(F)\)
\(P(M)=1-0.521=0.479\)

Answer:

a. \(P(F) = 0.521\), \(P(D)=0.108\), \(P(F\&D)=0.063\)
b. \(P(F\ or\ D)=0.566\), and \(56.6\%\) of adults are either female or divorced or both (Option D)
c. The probability that a randomly - selected adult is male is \(0.479\)