Question

# Suppose that in a year, 10% of all light vehicles (SUVs, pickups, passenger cars, and minivans)...

Suppose that in a year, 10% of all light vehicles (SUVs, pickups, passenger cars, and minivans) sold in the United States were pickups and 30% were passenger cars. Moreover, a randomly chosen vehicle sold that year was twice as likely to be an SUV as a minivan. Find the associated probability distribution.

 Outcome SUVs pickups passenger cars minivans Probability

SOLUTION:

From given data,

Suppose that in a year, 10% of all light vehicles (SUVs, pickups, passenger cars, and minivans) sold in the United States were pickups and 30% were passenger cars. Moreover, a randomly chosen vehicle sold that year was twice as likely to be an SUV as a minivan. Find the associated probability distribution.

Let ,

P(SUV) = 2x

P(minivan) = x = 0.2(from below calculation)

P(pickup) = 10% = 10/100 = 0.1

P(passenger car) = 30% = 30 / 100 =0.3

Therefore,

P(SUV) +P(pickup) + P(passenger car) +P(minivan) = 1

2x + 10/100 +  30 / 100 + x = 1

3x + 40 / 100 =1

3x = 1 - ( 40 / 100 )

3x = (100 -40) /100

3x = 60 /100

x = 20 / 100

x = 0.2

P(SUV) = 2x = 2*0.2 = 0.4

 Outcome SUVs pickups passenger cars minivans Probability 0.4 0.1 0.3 0.2