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

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