I am thinking of buying a used vehicle. I can choose from one of three types: a

Question

I am thinking of buying a used vehicle. I can choose from one of three types: a hatchback, a sedan, or an SUV. There are 9 hatchbacks I am considering, of which 3 have antilock brakes. There are 10 sedans I am considering, of which 6 have antilock brakes. There are 6 SUVs I am considering, of which 3 have antilock brakes.

(a) If I choose at random from all of the vehicles I am considering, what is the probability that the vehicle I choose will be an SUV with antilock brakes?

(b) If I first choose a type of vehicle at random and then choose a vehicle of that type at random, what is the probability that the vehicle I choose will be an SUV with antilock brakes?

Explanation / Answer

Ans: P(AB/HB)=3/9=0.33

P(AB/SD)=6/10=0.6

P(AB/SUV)=3/6=0.5

P(HB)=9/25

P(SD)=10/25

P(SUV)=6/25=0.24

P(not SUV)=1-0.24=0.76

a)P(SUV and AB)=P(AB/SUV)*P(SUV)=0.5*6/25=0.12

b)P(SUV/AB)=P(AB/SUV)*P(SUV)/[P(AB/SUV)*P(SUV)+P(AB/not SUV)*P(not SUV)]

=0.5*0.24/[0.5*0.24+0.47*0.76]

(Note :P(AB/not SUV)=(6+3)/(9+10)=9/19=0.47)

=0.12/[0.12+0.357]=0.12/0.477=0.25

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

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