The following table summarizes visits to emergency departments at four hospitals

Question

The following table summarizes visits to emergency departments at four hospitals People may leave without being seen by a physician, and those visits are denoted at LWBS. The remaining visits may result in admission to the hospital, or no admission (5 pts) Hospital 4 242 984 3103 4329 Total 953 4485 16814 22252 3 246 270 1558 5163 6991 195 1277 LWBS Admitted Not admitted 3280 Total 4728 5640 5292 Let A denote the event that a visit is to hospital 4 and B denote the event that a visit results in LWBS (at any hospital). Determine (a) P(AB) (b) P(A'B) (c) P(AB') (d) P(B A) (e) Are events A and B statistically independent? Why or why not?

Explanation / Answer

a)P(A|B) =242/953=0.2539

b) P(A'|B)=1-P(A|B) =1-0.2539 =0.7461

c) P(A|B') =(984+3103)/(4485+16814)=0.1919

d)P(B|A) =242/4329=0.0559

e) here as P(A) =4329/22252=0.1945

P(B) =953/22252=0.0428

therefore P(A)*P(B) =0.0083

also P(AnB) =242/22252 =0.0109

as P(AnB) is not equal to P(A)*P(B) ; A and B are not independent,

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