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.

MGS2150W07 final- Requires Respondus LockDown Browser

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?

查看解析

登录即可查看完整答案

类似问题

In a consumer society, many adults channel creativity into buying things

Economic stress and unpredictable times have resulted in a booming industry for self-help products

People born without creativity never can develop it

A product has a selling price of $20, a contribution margin ratio of 40% and fixed cost of $120,000. To make a profit of $30,000. The number of units that must be sold is: Type the number without $ and a comma. Eg: 20000

Which of the following statement regarding cost is correct:

Under the assumptions used in cost-volume-profit analysis, as the activity increases:

The CVP and break-even analysis are supported by a range of important assumptions. Which of the following is not an assumption of the CVP:

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

MGS*2150*W07 final- Requires Respondus LockDown Browser

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?

查看解析

登录即可查看完整答案

类似问题

In a consumer society, many adults channel creativity into buying things

Economic stress and unpredictable times have resulted in a booming industry for self-help products

People born without creativity never can develop it

A product has a selling price of $20, a contribution margin ratio of 40% and fixed cost of $120,000. To make a profit of $30,000. The number of units that must be sold is: Type the number without $ and a comma. Eg: 20000

Which of the following statement regarding cost is correct:

Under the assumptions used in cost-volume-profit analysis, as the activity increases:

The CVP and break-even analysis are supported by a range of important assumptions. Which of the following is not an assumption of the CVP:

更多留学生实用工具

希望你的学习变得更简单

MGS2150W07 final- Requires Respondus LockDown Browser