The probability of 3 red cars in a parking lot with 16 cars is 10%. What is the probability that in a random group of 5 cars one is red.
The probability of 3 red cars in a parking lot with 16 cars is 10%. The number of ways of picking 5 cars of the 16 is given by ``16C5. Of these, the number of ways of picking only 1 red car is 13C4*3C1, the number of ways of picking 2 red cars is 13C3*3C2 and the number of ways of picking 3 red cars is 13C2*3C3
The probability that one car is red in the group of 5 cars that is picked is:` (13C4*3C1 + 13C3*3C2 + 13C2*3C3)/(16C5) ~~ 0.7053` .
Multiplying this with the probability that the number of red cars in the 16 cars at the parking lot is 10%, the final probability is 0.07053.
The probability of a random group of cars having 1 red car that are picked from the parking lot is 0.07053.