Probability

[匿名]

2009-12-15 1:56 am

Q. 1
30 circuit boards, including 5 that are defective, are sent to service centre, from which 6 boards will be randomly selected and tested. Find the probability that at least 3 of the selected boards are defective

Q. 2
In a college, 66% of students're business majors and 16% are enginneering majors. Two thirds of business majors are females, while only one quarter of engineering majors are females.It's also known that half of all the other majors are females. A student is selected in the college. If the student selected is male, what's the probability that he's a business major?

回答 (1)

Prof. Physics

2009-12-15 2:57 am

✔ 最佳答案

1. P(at least 3 of the selected boards are defective)

= 1 - P(no boards are defective) - P(1 board is defective) - P(2 boards are defective)

= 1 - 25C6/30C6 - (25C5)(5C1)/30C6 - (25C4)(5C2)/30C6

= 0.0413 (cor. to 4 d.p.)

2. P(male) = P(business and male) + P(engineering and male) + P(others and male)

= (0.66)(1 - 2/3) + (0.16)(1 - 1/4) + (1 - 0.66 - 0.16)(1 - 1/2)

= 0.43

P(business and male) = 0.66(1 - 2/3) = 0.22

So, P(business major│male)

= P(business and male) / P(male)

= 0.22 / 0.43

= 22/43

參考: Physics king

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