Question

Attached below is the 2-way frequency table for patient group and gender, also called the joint frequency table. Use this data to answer question 1.

Patients	Female	Male
Trauma Patient	2	6
Volunteer	39	48

1. Calculate the following probabilities for a randomly selected patient from the study:
   1. They are a trauma patient AND they are male
   2. They are a volunteer GIVEN they are female

Answer 1

a. Let T = Event that the subject is a trauma patient

and M = Event that the subject is a male

Probability that the patient selected is a trauma patient and is a male

= P(TM)

= No. of patients who are trauma patients and are males / Total no. of subjects

= 6 / 95

= 0.0632

Probability that the patient selected is a trauma patient and is a male is 0.0632

b. Let V = Selected subject is a volunteer

F = Event that the selected subject is female

Probability that they are a volunteer GIVEN they are female

= P ( V | F)

= P(VF) / P(F)..................(Property of conditional probability)

From the 2x2 table,

= (39/95) / (41/95)

= (39/41)

= 0.9512

Probability that the patient selected is a volunteer GIVEN that the patient is a female is 0.9512.