Question

Consider the hospital emergency room data displayed below. Let A denote the event that a visit is to hospital 4, and let B denote the event that a visit results in LWBS (at any hospital). Determine the following probabilities. Round to three decimal places. Total Total LWBS Admitted Not admitted 3830 5299 6988 5642 4339 22268 196 1273 272 1552 5164 4729 956 4483 16829 244 244 989 3106 669 (a) PIAn B) (b) P(A (c) PIAUB)

Answer 1

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). (a) The event (A B) denotes a visit is to hospital 4, and it results in LWBS. The probability P(A B) is derived as follows: P(ANB)=2 Number of favourable cases Total number of outcomes 244 22268 = 0.011 (round to 3-decimal places) Thus, P(ANB)= 0.011 (b The event A denotes the event that a visit is to all other hospitals other than 4. It can be written as A' =1-A. The probability PA') is derived as follows: P(A')=1- P(A) Number of favourable cases Total number of outcomes 4339 =1- 22268 = 0.805 (round to 3-decimal places) Thus, P(A)= 0.805.

(c) The event (AUB) denotes a visit is to hospital 4, or it results in LWBS. The probability P(AUB) is derived as follows: P(AUB)=P(A)+P(B)-P(AB) So, Number of favourable cases P(4) = Total number of outcomes 4339 22268 B) = Number of favourable cases Total number of outcomes 956 22268 Number of favourable cases P(AB) = Total number of outcomes 244 22268 Thus, P(AUB) = P(A) + P(B)-P(A B ) 4339956 244 22268 22268 22268 5,051 22268 = 0.227 (round to 3-decimal places) Thus, P(A UB) = 0.227.