Answer:
0.31
Step-by-step explanation:
Given an ill person exhibits the symptoms H, find the probability that the person has illness I1.
So in other words, we need to find P (I1 | H).
We will make use of Baye's rule.
P (I1 | H) =
P(H) can be calculated using total law of probability.
P(H) = P (H | I1)*P(I1) + P (H | I2)*P(I2) + P (H | I3)*P(I3)
= (0.90)(0.01) + (0.95)*(0.05) + (0.75)*(0.02)
= 0.009 + 0.00475 + 0.015 =0.02875
P (H | I1)*P(I1) = (0.90)(0.01) = 0.009
so
P (I1 | H) = = = 0.31