Probability Examples on Bayes Theorem
In this class, We discuss Probability Examples on Bayes Theorem.
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Example 1:
Suppose five men out of a hundred and 25 women out of 10000 are color blind.
We choose a color-blind person at random.
What is the probability of the person being male?
Assume males and females are equal in number.
Solution:
P(M) = 1/2 and P(F) = 1/2
Male M and Female F are equal in number.
P(B|M) = 5/100 = 0.05
P(B|F) = 25/10000 = 0.0025
P(M|B) = (P(M)P(B|M))/(P(M)P(B|M) + P(F)P(B|F))
P(M|B) = (0.05 * 0.5)/((0.05 * 0.5) + (0.5 * 0.0025))
P(M|B) = 0.95
Example 2:
The chance that doctor A will diagnose a disease x correctly is 60%.
A patient’s chance of dying of disease x after correct diagnosis is 40%.
The chance of death after a wrong diagnosis is 70%.
A patient of doctor A died of disease x.
What is the chance of the disease being diagnosed correctly?
Solution:
Event D = Diagnoised properly
P(D) = 60/100 = 0.6
P(D’) = 1 – P(D) = 0.4.
P(Death|D) = 0.4
P(Death | D’) = 0.7
P(D|Death) = (P(D)P(Death|D))/(P(D)P(Death|D) + (P(D’)P(Death|D’))
P(D|Death) = (0.6 * 0.4)/((0.6 * 0.4) + (0.7 * 0.4))
P(D|Death) = 6/13