Question

In: Statistics and Probability

Admissions to the emergency department have been grouped by time of admission and patient problem. Counts...

Admissions to the emergency department have been grouped by time of admission and patient problem. Counts for the last week are as follows:

	Day	Evening	Night	Total
Minor injury	125	60	20	205
Abdominal pain	130	120	80	330
Other	210	170	140	520
Total	465	350	240	1055

A) What proportion of admissions are in the evening?

B) What proportion of admissions are in the evening and minor injuries?

C) What proportion of admissions are in the evening or minor injuries?

D) Among the admissions in the evening, what proportion are for minor injuries?

E) If the admission was for a minor injury, what proportion are in the evening?

F) Are “evening admission” and “minor injury” independent events? Use probability to justify the answer.

Expert Solution

We will be looking at the first 4 parts here:

a) The proportion of admissions that happen in the evening is computed here as:
= Total admissions in evening / Total number of admissions
= 350 / 1055
= 0.3318

Therefore 0.3318 is the required proportion here.

b) The proportion of admissions that are in the evening and minor injuries is computed here as:
= Total admissions in evening and minor injuries / Total number of admissions
= 60/1055
= 0.0569

Therefore 0.0569 is the required probability here.

c) The proportion of admissions are in the evening or minor injuries is computed using law of addition as:

P( evening ) + P(minor injuries ) - P(evening and minor injuries)

= (350 + 205 - 60) / 1055

= 0.4692

Therefore 0.4692 is the required proportion here.

d) Among the admissions in evening, proportion of minor injuries here are computed using Bayes theorem as:

P(minor injuries | evening) = P(minor injuries and evening) / P(evening)

= 60/350

= 0.1714

Therefore 0.1714 is the required probability here.

orchestra answered 1 year ago

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