This question has been regraded.

An urn contains two types of coins. Coin type A and coin type B. When a type A coin is flipped, it comes up heads with probability 1/4, whereas when a type B coin is flipped, it comes up heads with probability 3/4. A coin is randomly chosen from the urn and flipped. Given that the flip landed on heads, the probability that it was a type A coin is:

Question

This question has been regraded.

An urn contains two types of coins. Coin type A and coin type B. When a type A coin is flipped, it comes up heads with probability 1/4, whereas when a type B coin is flipped, it comes up heads with probability 3/4. A coin is randomly chosen from the urn and flipped. Given that the flip landed on heads, the probability that it was a type A coin is:

BlackTom AI · Accepted Answer

The problem describes an urn with two coin types, A and B, chosen at random. When type A is flipped, P(H|A) = 1/4; when type B is flipped, P(H|B) = 3/4. Since a coin is randomly chosen from the urn, we assume P(A) = P(B) = 1/2.

Step 1: Compute the overall probability of heads, P(H). Using the law of total probability: P(H) = P(H|A)P(A) + P(H|B)P(B) = (1/4)(1/2) + (3/4)(1/2) = 1/8 + 3/8 = 4/8 = 1/2.

Step 2: Apply Bayes' rule to find P(A|H): P(A|H) = [P(H|A)P(A)] / P(H) = [(1/4)(1/2)] / (1/2) = (1/8) / (1/2) = (1/8) × 2 = 1/4.

Even though the answer options are not provided in the prompt, this calculation shows how P(A|H) is determined given the stated probabilities and the equal prior for selecting coin types. The key ideas are the law of total probability to obtain P(H) and Bayes’ theorem to update the probability of having chosen type A after observing heads.

If you were listing options, you would expect the correct choice to be the one equal to 1/4, since it directly follows from the Bayes calculation above. The reasoning hinges on the equal prior for A and B and the different head probabilities for the two coin types.

STAT2011 (ND) Early Feedback Task (EFT)

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 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?

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?

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