Two taxi companies serve the city: the Red company operates 80% of the taxis and

Question

Two taxi companies serve the city: the Red company operates 80% of the taxis and
the Green the remaining 20%. A taxi is involved in a hit-and-run accident. Tests have
shown that witnesses correctly identify the colour of a taxi 80% of the time regardless
of the actual colour.
a) What is the probability the taxi is actually Red and is identified as Red by a
witness?
b) What is the probability the taxi is identified as Red?
c) Given the witness identified the taxi as Red, what is the probability it actually
was Red?
d) The Red company charges $1/kilometre and the Green charges $1.50. If you
choose taxis at random, what is the average amount/kilometre that you pay?

Explanation / Answer

a) probability the taxi is actually Red and is identified as Red by a witness =0.8*0.8 =0.64

b) probability the taxi is identified as Red =P(red and identified as red)+P(green and identified as red)

=0.8*0.8+0.2*(1-0.8)=0.68

c)

probability it actually was Red given identified the taxi as Red =P(red and identified as red)/P( identified as Red)

=0.8*0.8/0.68=0.9412

d)

average amount/kilometre that you pay =1*0.8+1.5*0.2=1.1

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.