Question 1 - General Probability Question. Consider the following questions based on the following data:

P (A=Hypertension) = 0.81

P (A=Hypertension B=Diabetes) = 0.35

P (B=Diabetes) = 0.43

1. What is the probability of Hypertension or B=Diabetes occurring, P(A=Hypertension=Diabetes)?

1. What is the probability of A=Hypertension occurring given that B=Diabetes has occurred (i.e. P (A=Hypertension|B=Diabetes)? That is to say, a person has Hypertension given they are diabetic.

1. Are the two events, Hypertension and Diabetes, disjoint (i.e. mutually exclusive)? Explain with values.

1. Are the two events independent? That is to say, is there evidence that having Hypertension influences presence of diabetes (or vice versa). Explain with values.

Question 2 General probability with Counts - Suppose you have the following Health Data on a group of patients who went to an OUHSC clinic in 2023.

Age \ Obesity	Normal Weight	Overweight/Obese	Totals
Under 45	347	749	1096
45 or Over	628	803	1431
Totals	975	1552	2527

a) What is the probability of overweight/obese given under 45? That is P(overweight/obese | Under 45)?

b) Are obesity and age independent of one another? Explain with your calculations.

c) What is P(Under 45 U Normal weight)? Show your calculation.