Question

a recent census found that 52.1% of adults are females, 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)=square ) (type an integer or a decimal. do not round.)

Explanation:

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

The formula for \(P(A\ or\ B)\) is \(P(A)+P(B)-P(A\&B)\). Here \(A = F\) and \(B = D\).
So \(P(F\ or\ D)=P(F)+P(D)-P(F\&D)\)

Step2: Substitute the values

We know \(P(F) = 0.521\), \(P(D)=0.108\) and \(P(F\&D)=0.063\)

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Answer:

\(P(F\ or\ D)=0.566\)

Interpretation: 56.6% of adults are either female or divorced.