A survey found that 60% of households own a dog (D), 40% own a cat (C), and 20% own both a dog and a cat (D∩C). What is the probability that a randomly selected household owns a dog, given that they own a cat?

Question

BlackTom AI · Accepted Answer

To start, we need to evaluate what the problem is asking: the probability that a randomly selected household owns a dog given that they own a cat, i.e., P(D|C).

First, recall the definition of conditional probability: P(D|C) = P(D ∩ C) / P(C).

From the survey data: P(D ∩ C) = 0.20 (households that own both a dog and a cat) and P(C) = 0.40 (households that own a cat).

Substituting these values into the formula gives P(D|C) = 0.20 / 0.40 = 0.5.

Thus, among households that own a cat, half also own a dog.

Why the other options aren’t correct:
- If you used P(D) = 0.60 in the numerator, you would be evaluating P(D) itself rather than the conditional event D given C, which ignores the information that the household already owns a cat.
- An answer of 0.33 would imply a ratio of 2/6 or 1/3, which would require different joint and marginal probabilities inconsistent with the given data.
- An answer of 0.6 would again reflect P(D) rather than P(D|C), mixing up unconditional and conditional probabilities.
- An answer of 0.2 would correspond to P(D ∩ C) itself, not the conditional probability given C.

Therefore, the correct conditional probability is 0.5, as calculated from P(D ∩ C) divided by P(C).

Statistics and Probability

A survey found that 60% of households own a dog (D), 40% own a cat (C), and 20% own both a dog and a cat (D∩C). What is the probability that a randomly selected household owns a dog, given that they own a cat?

查看解析

登录即可查看完整答案

类似问题

Question at position 7 CAEBD

Given that the first die shows a 3, what is the probability that S is an even number?

Given that S is 7, what is the probability that the first die showed 4 dots?

A bag contains 5 red balls and 5 blue balls. If you draw two balls without replacement, what is the probability that the second ball is red, given that the first ball was red?

If for two events [math: A] and [math: B] , [math: Pr(A)=920] Pr(A)= \frac{9}{20} , [math: Pr(B)=12] Pr(B)= \frac{1}{2} , and [math: Pr(A∩B)=15] Pr(A\cap B)= \frac{1}{5} , then [math: P(A|B)] is equal to :

A box contains 10 red, 5 green, and 10 blue marbles. A marble is chosen at random from the box, and it is noted that it is not one of the blue marbles. What is the probability that it is green?

Based on weather data collected in Racine, Wisconsin, on Christmas Day, the weather had the following distribution: Event Relative Frequency Clear & dry 0.20 Cloudy & dry 0.30 Rain 0.40 Snow 0.10 Supposing next Christmas is dry, determine the probability that it will also be cloudy.

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单