In a survey of students in a college, one question on thesurvey asks whether a s

Question

In a survey of students in a college, one question on thesurvey asks whether a student lives in a dorm on campus or livesoff campus. A second question asks for a rating of the foodservice. The results are:                         Excellent    Good      Fair    Poor Dorm                120            100       60       20 Off Campus       100            250       80       30 If a student is selected at random, find the following: 1) Probability a student lives in a dorm 2) P(excellent rating given dorm 3) P(dorm given a good rating) 4) P(excellent AND dorm) 5) P(excellent OR dorm) Please show work In a survey of students in a college, one question on thesurvey asks whether a student lives in a dorm on campus or livesoff campus. A second question asks for a rating of the foodservice. The results are:                         Excellent    Good      Fair    Poor Dorm                120            100       60       20 Off Campus       100            250       80       30 If a student is selected at random, find the following: 1) Probability a student lives in a dorm 2) P(excellent rating given dorm 3) P(dorm given a good rating) 4) P(excellent AND dorm) 5) P(excellent OR dorm) Please show work

Explanation / Answer

1) Probability a student lives in a dorm
(120+100+60+20)/760 = 0.3947

2) P(excellent rating given dorm
P(excellent | dorm) = P(excellent anddorm)/P(dorm) = 120/(120+100+60+20) = 0.4

3) P(dorm given a good rating)
P(dorm | good) = P(dorm and good)/P(good) =100/(100+250) = 0.2857

4) P(excellent AND dorm )
120/760 = 0.1579

5) P(excellent OR dorm)

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