researchers recorded data on pet ownership for randomly selected households in a large city. the venn…

researchers recorded data on pet ownership for randomly selected households in a large city. the venn diagram summarizes the data using events c: has a cat and d: has a dog.\nif a household that owns a cat is selected at random, what is the probability that the household owns a dog?\n(round to 4 decimal places. leave your answer in decimal form.)

researchers recorded data on pet ownership for randomly selected households in a large city. the venn diagram summarizes the data using events c: has a cat and d: has a dog.\nif a household that owns a cat is selected at random, what is the probability that the household owns a dog?\n(round to 4 decimal places. leave your answer in decimal form.)

Answer

Explanation:

Step1: Find the probability of owning a cat

The probability of owning a cat (P(C)) is the sum of the probability of only owning a cat and the probability of owning both a cat and a dog. Let (x) be the probability of owning both. The total probability of all events is (1). So (P(C)=x + 0.16). Also, (0.22+x + 0.16+0.46=1), which gives (x=1-(0.22 + 0.16+0.46)=0.16). Then (P(C)=0.16 + 0.16=0.32).

Step2: Use the formula for conditional probability

The formula for conditional probability is (P(D|C)=\frac{P(D\cap C)}{P(C)}). We know (P(D\cap C) = 0.16) (from Step 1) and (P(C)=0.32). So (P(D|C)=\frac{0.16}{0.32}=0.5)

Answer:

(0.5000)