Question

The BDW car dealership sells one sports model, the FX500. Of the customers who
buy this model, 40% choose red as the colour, 35% choose white, and 25% choose
black. Assume choice of colour is made independently by different customers.
a) Calculate the probability that among the next 10 customers who buy an FX500,
the first 6 will choose red cars and the next 4 will not choose red cars.
b) Calculate the probability that exactly one of the next 10 customers who buy an
FX500 will choose a black car.

Answer 1

) Calculate the probability that among the next 10 customers who buy an FX500, the first 6 will choose red cars and the next 4 will not choose red cars.

40% choose red as the color. This is same as the probability that any given customer chooses red car is

the probability that among the next 10 customers who buy an FX500, the first 6 will choose red cars and the next 4 will not choose red cars is

ans: the probability that among the next 10 customers who buy an FX500, the first 6 will choose red cars and the next 4 will not choose red cars is 0.0005

b) Calculate the probability that exactly one of the next 10 customers who buy an FX500 will choose a black car.

25% choose black. This is same as the probability that any given customer chooses black car is 0.25

Let X be the number of customers out of 10 who will choose a black car. We can say that X has a Binomial distribution with parameters, number of trials (number of customers) n=10 and success probability ( the probability that any given customer chooses black car) p=0.25

The probability that X=x of the next 10 customers who buy an FX500 will choose a black car is

The probability that exactly one of the next 10 customers who buy an FX500 will choose a black car is

ans: The probability that exactly one of the next 10 customers who buy an FX500 will choose a black car is 0.1877