# Thread: Probability Question - Can't figure out

1. ## Probability Question - Can't figure out

This seems like it should be easy but I can't get my mind around it:

"Of all the cars sold at a car dealership, 80% are not convertibles, 40% are red, and 5% are red convertibles. Given that a car sold by a salesperson at this dealership is a convertible, what is the probability that it is red?"

Any help would be appreciated, even if it's just a starting point.

Thanks!

2. Originally Posted by aliveiam
This seems like it should be easy but I can't get my mind around it:

"Of all the cars sold at a car dealership, 80% are not convertibles, 40% are red, and 5% are red convertibles. Given that a car sold by a salesperson at this dealership is a convertible, what is the probability that it is red?"

Any help would be appreciated, even if it's just a starting point.

Thanks!

If I understand this correctly....
Let R=red and C=convertible. You want

$\displaystyle P(R|C) ={P(RC)\over P(C)} ={.05\over .2} ={1\over 4}$.

3. Originally Posted by aliveiam
This seems like it should be easy but I can't get my mind around it:

"Of all the cars sold at a car dealership, 80% are not convertibles, 40% are red, and 5% are red convertibles. Given that a car sold by a salesperson at this dealership is a convertible, what is the probability that it is red?"

Any help would be appreciated, even if it's just a starting point.

Thanks!
Suppose there were 100 cars at the dealership. Since 80% of 100= 80 are NOT convertibles, 20 are convertibles. There are 5% of 100= 5 red convertibles so 5/20= 0.25 or 25% of the convertibles are red. The probability that a convertible is red is 0.25.