Question

Case	Hospitalized?	Gender	Age	Insured	Count of Patients
1	Yes	Male	>65	Yes	10
2	Yes	Male	<65	Yes	20
3	Yes	Female	>65	Yes	30
4	Yes	Female	<65	No	40
5	No	Male	>65	No	20
6	No	Male	<65	No	40
7	No	Female	>65	No	60
8	No	Female	<65	No	80

Using the above data answer the following questions:

1. What is the probability of hospitalization given that you are male? Select all males and count the number of patients who were hospitalized. Calculate the probability as the ratio of males hospitalized to number of males.
2. Create a contingency table for interaction between age and gender. Calculate the conditional probability of being female given that one is more than 65 years old. Also report the conditional probability of being 65 years old given that you are female. Answer this question by reducing the universe of possibilities to the condition specified. The condition is the event that we know has happened.

Answer 1

Probability of hospitalization given that you are male

= number of hospitalized males) / number of males

= 2 / 4

= 0.5

Contingency Table

Age/Gender	Male	Female
<65	2	2
>65	2	2

Conditional probability of being female given that one is more than 65 years old

= n(females more than 65 years old) / n(people more than 65 years old)

= 2 / 4

= 0.5

Conditional probability of being more than 65 years old given that you are female

= n(females more than 65 years old) / n(females)

= 2 / 4

= 0.5