Suppose that 30% students at WKU come from Zhejiang. 86% students from Zhejiang are majoring in business, and 70% students not from Zhejiang are majoring in business. What is the probability that a student who is majoring in business comes from Zhejiang?

Question

BlackTom AI · Accepted Answer

We start by identifying the given quantities and the goal. Let Z denote 'from Zhejiang' and B denote 'majoring in business.' We are given: P(Z) = 0.30, so P(not Z) = 0.70. Also P(B|Z) = 0.86 and P(B|not Z) = 0.70. We want P(Z|B), the probability a student is from Zhejiang given that they are majoring in business.

Use Bayes’ Rule: P(Z|B) = [P(B|Z) * P(Z)] / [P(B|Z) * P(Z) + P(B|not Z) * P(not Z)].

Compute the numerator: P(B|Z) * P(Z) = 0.86 * 0.30 = 0.258.
Compute the denominator: (P(B|Z) * P(Z)) + (P(B|not Z) * P(not Z)) = 0.258 + (0.70 * 0.70) = 0.258 + 0.49 = 0.748.
Divide the two: 0.258 / 0.748 ≈ 0.3446 (to four decimals, 0.3446; to three decimals, 0.345).

Now evaluate the provided options:
- Option: None of the other three. This would be correct only if none of the numeric values matches the calculation, which is not the case here since a numeric value matches closely.
- Option: ".3449". This is a numeric value extremely close to the computed probability (0.3446–0.3449 depending on rounding). Given typical rounding, 0.3446 rounds to 0.345, while 0.3449 is a plausible rounded value if one carries a slightly different intermediate rounding.
- Option: ".3066". This value would arise if either the numerator or denominator in Bayes’ formula were significantly different; it does not align with 0.258 / 0.748. Therefore this is not correct for the stated inputs.
- Option: ".2580". This matches the computed numerator before division, not the final probability P(Z|B); it would correspond to P(B|Z) * P(Z) alone, not the conditional probability given B. Hence this is not the right final value.

In summary, the calculation yields a final probability around 0.3446, which aligns most closely with the option listed as ".3449" when considering typical rounding conventions. The other numeric options correspond to intermediate quantities or misapplied steps and do not represent P(Z|B) given the data.

Suppose that 30% students at WKU come from Zhejiang. 86% students from Zhejiang are majoring in business, and 70% students not from Zhejiang are majoring in business. What is the probability that a student who is majoring in business comes from Zhejiang?单项选择题

类似问题

Name the Supreme Court decision that removed financial constraints on PACs.

Political scientists Joshua Kalla and David Broockman find that senior policy makers made themselves available to _____ between three and four times more often than they did to constituents.

Name the political scientist who argues that parties are designed to serve the needs of ambitious politicians (namely candidates and officeholders).

Name the political scientist who said this famous quote about the problems of pluralism: “The flaw in the pluralist heaven is that the heavenly choir sings with a strong upper-class accent.”

What is the name of the third party candidate in 2000 who was not allowed to participate in the presidential debates? Hint: We watched a video clip with him in class.

E.E. Schattshneider said, "Democracy is ________ save in terms of the parties."

Who was the most recently appointed justice to the Supreme Court?

更多留学生实用工具

智能学习助手

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