simple probability

[匿名]

2013-02-09 11:52 am

In a university, there are 120 students taking a statistics course. among them, 80 students come from the department of economics, while the rest come from the department of finance. in an exam, 10% of the economics students and 15% of the finance students receive an A grade.

Q: An examiner randomly inspects 2 exam papers with A grade so as to ensure they are properly marked. what are the probabilities of the following events happening?

1. 2 papers belong to students from the same department. (43/91)
2. 2 papers belong to students from different departments. (48/91)

please list out the steps needed to get the answers. thanks

回答 (1)

fooks

2013-02-09 5:54 pm

✔ 最佳答案

1.
E : a student gets A grade and comes from the department of economics
F : a student gets A grade and comes from the department of finance

Number of E = 80 x 10% = 8
Number of F = (120 - 80) x 15% = 6
Total number of E and F = 8 + 6 = 14

P(2 students from the same department)
= P(EE) + P(FF)
= [8C2 / 14C2] + [6C2/14C2]
= [(8!/6!2!) / (14!/12!2!)] + [(6!/4!2!) / (14!/12!2!)]
= (28/91) + (15/91)
= 43/91

2.
P(2 students from different departments)
= P(EF)
= 8C1 x 6C1 / 14C2
= (8!/7!1!) x (6!/5!1!) / (14!/12!2!)
= 8 x 6 / 91
= 48/91

參考: fooks

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