Question

In a car racing competition, four car brands are competing, each having two cars representing them. Cars from the same company have the same probability of winning. Each of the cars from Acura, Alfa Romeo and Audi has the same probability of winning the match, while each of Aston Martin’s cars has the probability of winning 1.66 times the probability of winning for each of the other brands’ cars.

(a) What is the chance of winning for each of the Aston Martin's cars?
Round your answer to one decimal place (e.g. 98.7).

(b) What is the chance of winning for each other cars?
Round your answer to one decimal place (e.g. 98.7).

(c) What is the probability of winning for Aston Martin brand?
Round your answer to one decimal place (e.g. 98.7).

(d) What is the probability of winning for each other brand?
Round your answer to one decimal place (e.g. 98.7).

Answer 1

Solution :

Given that :

In a car racing competition, four car brands are competing, each having two cars representing them. Cars from the same company have the same probability of winning.

We have different type of brands in cars.

i.e cars has the probability of winning 1.66 times the probability of winning for each of the other brands’ cars.

now assume the winning cars as "p"

Therefore probability of winning Aston matin,s car = 1.66 * p

these all probabilities will be added to 1

so that,now p + p + p + p + p + p + 1.66 p + 1.66 p = 1

9.32 p = 1

p = 1 / 9.32

p = 0.1073

a)What is the chance of winning for each of the Aston Martin's cars?

lets assume the winning car as 'x'

x = 1.66 * p

x = 1.66 * 0.1073

x = 0.178118(17.8 %)

b) What is the chance of winning for each other cars?

p = 0.1073 = 10.7%

c)What is the probability of winning for Aston Martin brand?

x = 0.178 + 0.178

x = 0.356

x = 35.6%

d)What is the probability of winning for each other brand?

x = 0.107 + 0.107

x = 0.214

x = 21.4 %