A parking lot has 100 red and blue cars in it. 40% of the cars are red. 70% of the red cars have radios. 80% of the blue cars have radios. What is the probability of selecting a car at random that is either red or has a radio?
40 (= 40% × 100) cars are red; 60 (= 100 − 40) cars are blue.
28 (= 70% × 40) cars are red with radios; 12 (= 40 − 28) cars are red without radios.
48 (= 80% × 60) cars are blue with radios; 12 (= 60 − 48) cars are blue without radios.
You succeed if you select a red car (40) or a blue car with a radio (48); there are 88 (=40 + 48) such cars.
Alternatively, you fail if you select a blue car without a radio (12); that leaves 100 − 12 = 88 successes.
The probability is 88 / 100 = 0.88 = 88%.
Thanks ver much. But i have one doubt that question says “probability of selecting a car at random that is either red or has a radio”, so why we cant choose red car with radio in place of blue car with radio?
We can.
Look at the numbers: red cars without radios, red cars with radios, blue cars with radios.
Thanks a lot
My pleasure.
One serious suggestion, i want from you. I am full time working in one company which is no where related to CFA level 1 prep or no where related to LOS. Daily i am studying 1 hr in morning before going office and after coming from office i am studying approx 2hrs and on weekends i get time. My job timing incl travel is approx 13 hrs. Can you please suggest me or what is your opinion of planning to quit job ad study for Level 1 and is it worth? Please help, i am in dilemma