Probabilities

CFA Level I Quant
#1

Hi everyone,

Can someone please explain how to calculate the below? Specificially the probability of radios? Thanks

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?

#2

P(red or radio) = P(red)+P(radio)-P(red and radio)

P(red): 0.4 given

P(radio): total probability of blue or red with radio: 0.4*0.7+0.6*0.8=0.76

P(red and radio): 0.4*0.7=0.28

answer is: 0.4+0.76-0.28=0.88

Is this the answer?

(to be honest I’m so tired I can’t solve simple things…)

#3

Yep

#4

thanks dude

#5

Here’s another way of getting to the same answer. It’s a bit longer than Moosey’s approach, but it also works:

P(red or radio) = P(red) + P(blue and radio)

= P(red) + P(blue)xP(radio|blue) = 0.40 + 0.60(0.80) = 0.88

#6

And another way:

P(red or radio) = 1 – P(blue and no radio)

= 1 – P(blue)P(no radio | blue)

= 1 – (0.6)(0.2)

= 1 – 0.12

= 0.88

#7

/doffs hat to S2000/