Cars are either​ race-car fast, slightly​ fast, or normal. It turns out that ​10% of all cars are​ race-car fast, ​40% are slightly​ fast, and 5% are normal. Of those that are​ race-car fast ​70% are​ red, as are ​45% of those that are slightly​ fast, and ​30% of those that are normal. what is the probability that a randomly selected car is red given that it is normal?

Probability = 37.5%

Step-by-step explanation:

Prob (Race fast) = 10%, Prob (Slight Fast) = 40%, Prob (Normal Car) = 50%

Prob (Red Car) = 70% of race fast cars, & 45% of slight fast cars, & 30% of Normal cars, & = (70% x 10%) + (45% x 40%) + (30% x 50%) = 7% + 18% + 15% = 40%

Prob (Normal & Red Car) = 30% of 50%  = 15%

Prob (Red car I Normal car) = Prob (Red & Normal Car I Normal Car) =  15% / 40% = 37.5%