Question

according to internal revenue service records, 1.92% of all household tax returns are audited. according to the humane society, 35% of all households own a dog. assuming dog ownership and audits are independent events, what is the probability a randomly selected household is audited and owns a dog? the probability is (round to six decimal places as needed.)

Explanation:

Step1: Convert percentages to decimals

Let \(A\) be the event that a household is audited, \(P(A)=0.0192\). Let \(D\) be the event that a household owns a dog, \(P(D) = 0.35\).

Step2: Use the formula for independent events

For independent events \(A\) and \(D\), \(P(A\cap D)=P(A)\times P(D)\).
Substitute the values: \(P(A\cap D)=0.0192\times0.35\).
Calculate \(0.0192\times0.35 = 0.00672\).

Answer:

\(0.006720\)