Could someone help me with this probability question?

allyb17

Hi, I think I am missing something kind of obvious here, my head is wrecked from orals so I'm not at my most alert!
"In a certain city, 60% of cars are from country A, 30% are from country B and 10% are from C.30% of cars from country A, 25% of cars from country B and 20% of cars from country C last for 10 years or more".
find the probability that:
(i) A car, bought at random in this city will last for 10 years or more.
(ii) A car will last for 10 years or more given that it is NOT from country A
(iii) A car is from country C given that it is 10 years old.

I have answered part (i):
A: 0.3 X 0.6=0.18
B: 0.25 X 0.3=0.075
C: 0.2 X 0.1= 0.02
Adding the probabilities=0.275 chance which corresponds to text book

the next answers are (ii)=0.2375 and (iii)=0.072

Cannot get the next 2

robman60

Hi, you've done the first part correctly. Here's how to do the next two parts.

(ii) If it is not from country A, it is from the remaining 40% of cars. From part i, we've worked out that 7.5% of cars from B last ten years and 2% from C last ten years. 7.5+2.5=9.5 -> 9.5/40=0.2375

(iii) Also from part i, we can see that 27.5% of cars last ten years or more. 2% of these are from country C. Therefore .02/.275=.0727272

Let me know if you still don't understand and I'll try to explain it.

allyb17

Thanks a million!