Lecture 10- Probability Trees

Question 1

In a particular hospital population, the probability a patient has high blood
pressure given they are diabetic is 0.85. If 10% of the patients are diabetic
and 25% have high blood pressure,
i) find the probability a patient has both diabetes and high blood
pressure.
ii)are the conditions of diabetes and high blood pressure independent?

Answer 1

i) 0.085
ii) they are not independent

See working in slides

Question 2

In tree diagrams…
Vertically you:
Across you:

Answer 2

Add

Multiply

Question 3

Suppose
F = being female
F¯ = being not female
R = being right-handed
R¯ = being not right-handed

Draw a tree diagram to reflect this…

Answer 3

look at slides for answer

Question 4

What is the probability that a randomly selected individual will be
right-handed?

Answer 4

Pr(R) = 0.8906

need info in the lecture slides to answer + working is there

Question 5

What is the probability that an individual is female given they are
right-handed? Recall Pr(F|R) ̸= Pr(R|F)

Answer 5

= 0.5701

again refer to lecture slides

Question 6

A hospital runs a clinic for patients with diabetes.
Consider the first 3 patients arriving in the clinic on a given date.
It is known that the probability of a patient coming to the clinic
having high blood pressure is 0.4.
Suppose X represents the number of patients out of three who have
high blood pressure:
X can take values 0, 1, 2, or 3.
Find the probabilities that 0, 1, 2, or 3 of the 3 patients have high blood
pressure.
T is the event ‘patient has high blood pressure’ and T¯ is the
complementary event ‘patient does not have high blood pressure’. The
population this clinic serves is large enough to assume independence.

Answer 6

Answers on slides

Question 7

What does independence mean in terms of a probability tree?

Answer 7

If events in the tree are independent it means that the probability of each branch is unaffected by the branches that come before. Being dependent is the opposite to this.