Question

A witness identified a suspect as having blond hair. However, when tested under lighting conditions similar to those on the night of the incident, it was concluded that the probability of correctly identifying blond hair was 0.90 and the probability of being incorrect about non-blond hair was 0.2. Suppose that 0.4 is the proportion of persons with blond hair that live in the area. Let two events A and B be defined as A = [ Identified as blond and B = [ Person is blond] 1. Fill in the four probabilities, and the marginal totals, in the two-way table. using... (A, B, Not A, Not B) 2. Given that this person was identified as blond, find the probability of being blond 3. Make a Venn diagram to display the relations among these two events.

Answer 1

Answer:

To get the table we have to find the following probabilities

p(A), p(B), p(not A), p(not B)

A = suspect has blond hair

B = suspect is blond

p(B) = 0.4

probability of identifying correctly = AIB = 0.90

prob of wrongful identification =  AlB' = 0.2

Probability of A = p(AIB) *p(B) + p(AIB')*p(B')

= 0.9 * 0.4 + 0.2 *(1-0.4)

= 0.48

p( not A) = 1-0.48 = 0.52

p(not b) = 1-0.40 = 0.6

the table  has been added as an attachment

2. probability of being blond = 0.9 * 0.4 / 0.48 = 0.75

3. p(A∩B) =  0 .90 * 0.4 = 0.36

the venn diagrams an attachment also