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.

4. 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) ital 270 1558 5163 6991 Total 953 4485 16814 225 195 47 984 3103 4329 LWBS Admitted_1277 Not admitted 3280 4728 5640 Total 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(AB) (c) P(AB) (d) P(BA) (e) Are events A and B statistically independent? Why or why not?

Explanation / Answer

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1.

a.P(A|B) = P(visits hospital 4 | visit results in LWBS)

= All visiting hospital 4 and LWBS/ total LWBS

= 242 / 953

= .254

b. P(A'|B) = 1-242/953 = 1-.254 = .746

c. P(A|B') = (984+3103)/(4485+16814) = .192

d. P(B|A)

= All visintg hospital 4 and LWBS / total visting hospital 4

= 242/4329

=.056

e. Are A and B statistically independent - Lets check this.

If P( A and B) = P(A)*P(B), then they are. otherwise they aren't

P(A and B) = 242/22252 = .011

P(A) = 4329/22252, P(B) = 953/22252 = .0428, P(A)*P(B) = .00833

Since, P(A)*P(B) is not equal to P(A and B) therefore they aren't independent

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