Problem 4 point In a certain community, the probability that a family owns a dog

Question

Problem 4 point In a certain community, the probability that a family owns a dog is 35%. Given that a family owns a dog the p bility that they also o na at sa itis also now that of all the m lies in a cat What is the probability that a randomly selected family owns a cat? What is the conditional probability that a randomly selected family owns a dog given that it owns a cat? Hint: Write out each of the probabilities you've been given in probability notation, as well as the probabilities you need to find. You may need to find a joint probability (P(A and B)) before you can answer the 2nd question. It may help to draw a Venn Diagram. Be sure to give your answers to at least 4 decimal places

Explanation / Answer

P( own dog) = 0.35 , P( Own Cat | Own dog) = 0.20, P(Own cat) = 0.37

a)

P( Own cat) = 0.37

Probability that randomly selected family own a cat = 0.37

b)

We use conditional formula,

P(A | B) = P(A AND B) / P(B)

Therefore,

P( Own Cat | Own dog) = P( Own Cat AND Dog) / P( Own dog)

0.20 = P( Own Cat AND Dog) / 0.35

P( Own Cat AND Dog) = 0.20 * 0.35

P( Own Cat AND Dog) = 0.07

Therefore,

P( Own Dog | Own cat) = P( Own Cat AND Dog) / P(Own cat)

= 0.07 / 0.37

= 0.189189

= 0.1892 (Rounded to four decimal places)

Conditional probability that randomly selected family owns a dog given that it owns a cat = 0.1892

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.